http://geometrie.idea-sketch.com/index.php?action=history&feed=atom&title=Erzeugendensystem_2012_13 2026-08-02T12:13:42Z Versionsgeschichte dieser Seite in Geometrie-Wiki MediaWiki 1.43.9 http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=21252&oldid=prev 2013-01-31T15:40:59Z

<p><span class="autocomment">Erzeugendensystem, Basis und Hülle</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 31. Januar 2013, 15:40 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Zeile 19:</td> <td colspan="2" class="diff-lineno">Zeile 19:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Menge der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; kann linear abhängig sein.&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Menge der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; kann linear abhängig sein.&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Def.(Basis)&#039;&#039;&#039;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Def.(Basis)&#039;&#039;&#039;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Eine </del>Basis <del style="font-weight: bold; text-decoration: none;">des Vektorraumes V ist </del>ein <del style="font-weight: bold; text-decoration: none;">minimales </del>Erzeugendensystem.&lt;br /&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">B ist eine </ins>Basis<ins style="font-weight: bold; text-decoration: none;">, wenn B </ins>ein Erzeugendensystem <ins style="font-weight: bold; text-decoration: none;">ist und linear unabhängig</ins>.&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Das bedeutet</del>, dass <del style="font-weight: bold; text-decoration: none;">die Menge der Vektoren, welche das </del>Erzeugendensystem <del style="font-weight: bold; text-decoration: none;">bilden linear unabhängig </del>ist.&lt;br /&gt;<del style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Daraus folgt</ins>, dass <ins style="font-weight: bold; text-decoration: none;">eine Basis eines Vektorraumes V ein minimales </ins>Erzeugendensystem ist.&lt;br /&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">--[[Benutzer:Jessy*|Jessy*]] 17:12, 18. Jan. 2013 (CET)&lt;br /&gt;&lt;br /&gt;</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">|}</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">&lt;/div&gt;</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20310:rev-21252:php=table --> </table>

Cplicht http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20310&oldid=prev 2013-01-18T16:14:10Z

<p><span class="autocomment">Erzeugendensystem, Basis und Hülle</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2013, 16:14 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Zeile 16:</td> <td colspan="2" class="diff-lineno">Zeile 16:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Def.(Erzeugendensystem)&#039;&#039;&#039;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Def.(Erzeugendensystem)&#039;&#039;&#039;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Eine Menge von Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist ein Erzeugendensystem enes Vektorraumes V, wenn V eine Teilmenge der linearen Hülle von &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist.&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Eine Menge von Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist ein Erzeugendensystem enes Vektorraumes V, wenn V eine Teilmenge der linearen Hülle von &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist.&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Das heißt, wenn man mit den Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; alle Vektoren des Vektorraumes V darstellen kann ist die Menge der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ein Erzeugendensystem von V.&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Das heißt, wenn man mit den Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; alle Vektoren des Vektorraumes V darstellen kann ist die Menge der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ein Erzeugendensystem von V<ins style="font-weight: bold; text-decoration: none;">.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Die Menge der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; kann linear abhängig sein</ins>.&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Def.(Basis)&#039;&#039;&#039;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Def.(Basis)&#039;&#039;&#039;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Eine Basis des Vektorraumes V ist ein minimales Erzeugendensystem.&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Eine Basis des Vektorraumes V ist ein minimales Erzeugendensystem.&lt;br /&gt;</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20309:rev-20310:php=table --> </table>

Jessy* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20309&oldid=prev 2013-01-18T16:12:40Z

<p><span class="autocomment">Erzeugendensystem, Basis und Hülle</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2013, 16:12 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Zeile 11:</td> <td colspan="2" class="diff-lineno">Zeile 11:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;843&quot; height=&quot;581&quot;  version=&quot;4.2&quot; ggbBase64=&quot;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&quot; 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showResetIcon = &quot;false&quot; enableRightClick = &quot;false&quot; errorDialogsActive = &quot;true&quot; enableLabelDrags = &quot;false&quot; showMenuBar = &quot;false&quot; showToolBar = &quot;false&quot; showToolBarHelp = &quot;false&quot; showAlgebraInput = &quot;false&quot; useBrowserForJS = &quot;true&quot; allowRescaling = &quot;true&quot; /&gt;&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Erzeugendensystem, Basis und Hülle=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Erzeugendensystem, Basis und Hülle=</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Def.(lineare Hülle)'''&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Lineare Hülle der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist die Menge der Linearkombinationen von &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Das bedeutet, die lineare Hülle der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; enthält alle Vektoren, die man mithilfe der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; darstellen kann.&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Def.(Erzeugendensystem)'''&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Eine Menge von Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist ein Erzeugendensystem enes Vektorraumes V, wenn V eine Teilmenge der linearen Hülle von &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ist.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Das heißt, wenn man mit den Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; alle Vektoren des Vektorraumes V darstellen kann ist die Menge der Vektoren &lt;math&gt; \vec{a_1}, \vec{a_2}, ..., \vec{a_n} &lt;/math&gt; ein Erzeugendensystem von V.&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Def.(Basis)'''&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Eine Basis des Vektorraumes V ist ein minimales Erzeugendensystem.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Das bedeutet, dass die Menge der Vektoren, welche das Erzeugendensystem bilden linear unabhängig ist.&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">--[[Benutzer:Jessy*|Jessy*]] 17:12, 18. Jan. 2013 (CET)&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20308:rev-20309:php=table --> </table>

Jessy* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20308&oldid=prev 2013-01-18T16:02:30Z

<p><span class="autocomment">Beispiel 2</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2013, 16:02 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9">Zeile 9:</td> <td colspan="2" class="diff-lineno">Zeile 9:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}\right}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die Menge aller Pfeilklassen der Ebene. (Strg+f frischt den Bildschirm auf)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}\right}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die Menge aller Pfeilklassen der Ebene. (Strg+f frischt den Bildschirm auf)</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 2=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 2=</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width="843" height="581"  version="4.2" ggbBase64="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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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text-decoration: none;">&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=Erzeugendensystem, Basis und Hülle=</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20242:rev-20308:php=table --> </table>

Jessy* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20242&oldid=prev 2013-01-16T17:49:01Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2013, 17:49 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8">Zeile 8:</td> <td colspan="2" class="diff-lineno">Zeile 8:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}\right}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die Menge aller Pfeilklassen der Ebene. (Strg+f frischt den Bildschirm auf)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}\right}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die Menge aller Pfeilklassen der Ebene. (Strg+f frischt den Bildschirm auf)</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=Beispiel 2=</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="843" height="581"  version="4.2" ggbBase64="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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--- hier drunter nichts eintragen ---&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Linalg]]</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20223:rev-20242:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20223&oldid=prev 2013-01-16T16:07:43Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2013, 16:07 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;div style="margin:0; margin-right:4px; border:1px solid #27408B; padding: 1em 1em 1em 1em; background-color:#B9D0F0; align:left;"&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{|width=90%| style="background-color:#B9D0F0; padding:1em"</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| valign="top" |</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;!--- hier drüber nichts eintragen ---&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 1=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 1=</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1269&quot; 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showResetIcon = &quot;false&quot; enableRightClick = &quot;false&quot; errorDialogsActive = &quot;true&quot; enableLabelDrags = &quot;false&quot; showMenuBar = &quot;false&quot; showToolBar = &quot;false&quot; showToolBarHelp = &quot;false&quot; showAlgebraInput = &quot;false&quot; useBrowserForJS = &quot;true&quot; allowRescaling = &quot;true&quot; /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}\right}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die Menge aller Pfeilklassen der Ebene. (Strg+f frischt den Bildschirm auf)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}\right}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die Menge aller Pfeilklassen der Ebene. (Strg+f frischt den Bildschirm auf)</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;!--- hier drunter nichts eintragen ---&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Kategorie:Linalg]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;/div&gt;</ins></div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20219:rev-20223:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20219&oldid=prev 2013-01-16T15:57:24Z

<p><span class="autocomment">Beispiel 1</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2013, 15:57 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Zeile 2:</td> <td colspan="2" class="diff-lineno">Zeile 2:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1269&quot; height=&quot;851&quot;  version=&quot;4.2&quot; ggbBase64=&quot;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&quot; showResetIcon = &quot;false&quot; enableRightClick = &quot;false&quot; errorDialogsActive = &quot;true&quot; enableLabelDrags = &quot;false&quot; showMenuBar = &quot;false&quot; showToolBar = &quot;false&quot; showToolBarHelp = &quot;false&quot; showAlgebraInput = &quot;false&quot; useBrowserForJS = &quot;true&quot; allowRescaling = &quot;true&quot; /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1269&quot; height=&quot;851&quot;  version=&quot;4.2&quot; ggbBase64=&quot;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&quot; showResetIcon = &quot;false&quot; enableRightClick = &quot;false&quot; errorDialogsActive = &quot;true&quot; enableLabelDrags = &quot;false&quot; showMenuBar = &quot;false&quot; showToolBar = &quot;false&quot; showToolBarHelp = &quot;false&quot; showAlgebraInput = &quot;false&quot; useBrowserForJS = &quot;true&quot; allowRescaling = &quot;true&quot; /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die <del style="font-weight: bold; text-decoration: none;">menge </del>aller Pfeilklassen der Ebene.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b<ins style="font-weight: bold; text-decoration: none;">}\right</ins>}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die <ins style="font-weight: bold; text-decoration: none;">Menge </ins>aller Pfeilklassen der Ebene. <ins style="font-weight: bold; text-decoration: none;">(Strg+f frischt den Bildschirm auf)</ins></div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20218:rev-20219:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20218&oldid=prev 2013-01-16T15:56:26Z

<p><span class="autocomment">Beispiel 1</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2013, 15:56 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 1=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 1=</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1269&quot; 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showResetIcon = &quot;false&quot; enableRightClick = &quot;false&quot; errorDialogsActive = &quot;true&quot; enableLabelDrags = &quot;false&quot; showMenuBar = &quot;false&quot; showToolBar = &quot;false&quot; showToolBarHelp = &quot;false&quot; showAlgebraInput = &quot;false&quot; useBrowserForJS = &quot;true&quot; allowRescaling = &quot;true&quot; /&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Experimentieren Sie: Wann ist die Menge &lt;math&gt;\left{\vec{a}, \vec{b}&lt;/math&gt; ein Erzeugendensystem für den &lt;math&gt;\mathbb{R}^2&lt;/math&gt; bzw. für die menge aller Pfeilklassen der Ebene.</ins></div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20217:rev-20218:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20217&oldid=prev 2013-01-16T15:53:35Z

<p><span class="autocomment">Beispiel 1</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2013, 15:53 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 1=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Beispiel 1=</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; 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*m.g.* http://geometrie.idea-sketch.com/index.php?title=Erzeugendensystem_2012_13&diff=20216&oldid=prev 2013-01-16T15:53:26Z

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