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Lösning till övning 3 - Versionshistorik
2026-04-06T10:21:34Z
Versionshistorik för denna sida på wikin
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Geoba den 15 augusti 2008 kl. 08.45
2008-08-15T08:45:09Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.45</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 12:</td>
<td colspan="2" class="diff-lineno">Rad 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><center><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=</math></center></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\begin{align}</ins>G(\lambda\boldsymbol{u})<ins style="color: red; font-weight: bold; text-decoration: none;">&</ins>=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}<ins style="color: red; font-weight: bold; text-decoration: none;">\\</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&</ins>=<ins style="color: red; font-weight: bold; text-decoration: none;">\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq\lambda G(\boldsymbol{u}).\end{align}</ins></math></center></div></td></tr>
</table>
Geoba
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Geoba den 15 augusti 2008 kl. 08.42
2008-08-15T08:42:26Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
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<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.42</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 9:</td>
<td colspan="2" class="diff-lineno">Rad 9:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Avbildningen <math>G</math> är inte linjär, ty </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Avbildningen <math>G</math> är inte linjär, ty </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</<del style="color: red; font-weight: bold; text-decoration: none;">center</del>></<del style="color: red; font-weight: bold; text-decoration: none;">math</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>></<ins style="color: red; font-weight: bold; text-decoration: none;">center</ins>></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=<del style="color: red; font-weight: bold; text-decoration: none;">\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq\lambda G(\boldsymbol{u}).</del></math></center></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=</math></center></div></td></tr>
</table>
Geoba
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Geoba den 15 augusti 2008 kl. 08.41
2008-08-15T08:41:28Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.41</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Låt <math>\boldsymbol{u}=\underline{\boldsymbol{e}}X_1=\underline{\boldsymbol{e}}\begin{pmatrix}{a_1}\\{b_1}\\{c_1}\end{pmatrix}</math> och <math>\boldsymbol{v}=\underline{\boldsymbol{e}}X_2=\underline{\boldsymbol{e}}\begin{pmatrix}{a_2}\\{b_2}\\{c_2}\end{pmatrix}</math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Låt <math>\boldsymbol{u}=\underline{\boldsymbol{e}}X_1=\underline{\boldsymbol{e}}\begin{pmatrix}{a_1}\\{b_1}\\{c_1}\end{pmatrix}</math> och <math>\boldsymbol{v}=\underline{\boldsymbol{e}}X_2=\underline{\boldsymbol{e}}\begin{pmatrix}{a_2}\\{b_2}\\{c_2}\end{pmatrix}</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Vi behöver summan</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Vi behöver summan</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><center><math>\boldsymbol{u}+\boldsymbol{v}=\underline{\boldsymbol{e}}\begin{pmatrix}{a_1}\\{b_1}\\{c_1}\end{pmatrix}+\underline{\boldsymbol{e}}\begin{pmatrix}{a_2}\\{b_2}\\{c_2}\end{pmatrix}=\underline{\boldsymbol{e}}\begin{pmatrix}{a_1+a_2}\\{b_1+b_2}\\{c_1+c_2}\end{pmatrix}</<del style="color: red; font-weight: bold; text-decoration: none;">center</del>></<del style="color: red; font-weight: bold; text-decoration: none;">math</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><center><math>\boldsymbol{u}+\boldsymbol{v}=\underline{\boldsymbol{e}}\begin{pmatrix}{a_1}\\{b_1}\\{c_1}\end{pmatrix}+\underline{\boldsymbol{e}}\begin{pmatrix}{a_2}\\{b_2}\\{c_2}\end{pmatrix}=\underline{\boldsymbol{e}}\begin{pmatrix}{a_1+a_2}\\{b_1+b_2}\\{c_1+c_2}\end{pmatrix}</<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>></<ins style="color: red; font-weight: bold; text-decoration: none;">center</ins>></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>och</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>och</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math></div></td></tr>
<tr><td colspan="2" class="diff-lineno">Rad 7:</td>
<td colspan="2" class="diff-lineno">Rad 7:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>a_1}\\{\lambda b_1}\\{\lambda </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>a_1}\\{\lambda b_1}\\{\lambda </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>c_1}\end{pmatrix}.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>c_1}\end{pmatrix}.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></<del style="color: red; font-weight: bold; text-decoration: none;">center</del>></<del style="color: red; font-weight: bold; text-decoration: none;">math</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>></<ins style="color: red; font-weight: bold; text-decoration: none;">center</ins>></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Avbildningen <math>G</math> är inte linjär, ty </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Avbildningen <math>G</math> är inte linjär, ty </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</center></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</center></math></div></td></tr>
<tr><td colspan="2" class="diff-lineno">Rad 13:</td>
<td colspan="2" class="diff-lineno">Rad 13:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq\lambda G(\boldsymbol{u}).</<del style="color: red; font-weight: bold; text-decoration: none;">center</del>></<del style="color: red; font-weight: bold; text-decoration: none;">math</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq\lambda G(\boldsymbol{u}).</<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>></<ins style="color: red; font-weight: bold; text-decoration: none;">center</ins>></div></td></tr>
</table>
Geoba
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Geoba den 15 augusti 2008 kl. 08.36
2008-08-15T08:36:38Z
<p></p>
<table style="background-color: white; color:black;">
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<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.36</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 11:</td>
<td colspan="2" class="diff-lineno">Rad 11:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</center></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</center></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}</center></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}<ins style="color: red; font-weight: bold; text-decoration: none;">\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq\lambda G(\boldsymbol{u}).</ins></center></math></div></td></tr>
</table>
Geoba
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Geoba den 15 augusti 2008 kl. 08.35
2008-08-15T08:35:57Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.35</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 12:</td>
<td colspan="2" class="diff-lineno">Rad 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}<del style="color: red; font-weight: bold; text-decoration: none;">\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq\lambda G(\boldsymbol{u}).</del></center></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}</center></math></div></td></tr>
</table>
Geoba
http://wiki.math.se/wikis/samverkan/linalg-LIU/index.php?title=L%C3%B6sning_till_%C3%B6vning_3&diff=222&oldid=prev
Geoba den 15 augusti 2008 kl. 08.35
2008-08-15T08:35:33Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.35</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 12:</td>
<td colspan="2" class="diff-lineno">Rad 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq .</center></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq<ins style="color: red; font-weight: bold; text-decoration: none;">\lambda G(\boldsymbol{u})</ins>.</center></math></div></td></tr>
</table>
Geoba
http://wiki.math.se/wikis/samverkan/linalg-LIU/index.php?title=L%C3%B6sning_till_%C3%B6vning_3&diff=221&oldid=prev
Geoba den 15 augusti 2008 kl. 08.33
2008-08-15T08:33:25Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.33</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 12:</td>
<td colspan="2" class="diff-lineno">Rad 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\<del style="color: red; font-weight: bold; text-decoration: none;">neq </del>\lambda <del style="color: red; font-weight: bold; text-decoration: none;">G(</del>\<del style="color: red; font-weight: bold; text-decoration: none;">boldsymbol</del>{<del style="color: red; font-weight: bold; text-decoration: none;">u</del>}<del style="color: red; font-weight: bold; text-decoration: none;">)</del>.</center></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\<ins style="color: red; font-weight: bold; text-decoration: none;">begin{pmatrix}{</ins>\lambda <ins style="color: red; font-weight: bold; text-decoration: none;">a_1c_1}\</ins>\{<ins style="color: red; font-weight: bold; text-decoration: none;">\lambda b_1^2</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">\\{b_1+c_1}\end{pmatrix}\neq </ins>.</center></math></div></td></tr>
</table>
Geoba
http://wiki.math.se/wikis/samverkan/linalg-LIU/index.php?title=L%C3%B6sning_till_%C3%B6vning_3&diff=220&oldid=prev
Geoba den 15 augusti 2008 kl. 08.32
2008-08-15T08:32:46Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.32</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 12:</td>
<td colspan="2" class="diff-lineno">Rad 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=</center></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=<ins style="color: red; font-weight: bold; text-decoration: none;">\lambda\underline{\boldsymbol{e}}\neq \lambda G(\boldsymbol{u}).</ins></center></math></div></td></tr>
</table>
Geoba
http://wiki.math.se/wikis/samverkan/linalg-LIU/index.php?title=L%C3%B6sning_till_%C3%B6vning_3&diff=219&oldid=prev
Geoba den 15 augusti 2008 kl. 08.32
2008-08-15T08:32:22Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.32</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 12:</td>
<td colspan="2" class="diff-lineno">Rad 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\cdot\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=<del style="color: red; font-weight: bold; text-decoration: none;">\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq \lambda G(\boldsymbol{u}).</del></center></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=</center></math></div></td></tr>
</table>
Geoba
http://wiki.math.se/wikis/samverkan/linalg-LIU/index.php?title=L%C3%B6sning_till_%C3%B6vning_3&diff=218&oldid=prev
Geoba den 15 augusti 2008 kl. 08.30
2008-08-15T08:30:59Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 augusti 2008 kl. 08.30</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Rad 11:</td>
<td colspan="2" class="diff-lineno">Rad 11:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</center></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> <center><math>1.\quad G(\boldsymbol{u}+\boldsymbol{v})\neq G(\boldsymbol{u})+G(\boldsymbol{v})\qquad\qquad 2.\quad G(\lambda\boldsymbol{u})\neq\lambda G(\boldsymbol{u}).</center></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>T.ex., följer att</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\<del style="color: red; font-weight: bold; text-decoration: none;">middot</del>\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><center><math>G(\lambda\boldsymbol{u})=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=G\left(\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1}\\{\lambda b_1}\\{\lambda c_1}\end{pmatrix}\right)=\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\lambda c_1}\\{\lambda^2b_1^2}\\{\lambda b_1+\lambda c_1}\end{pmatrix}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq \lambda G(\boldsymbol{u}).</center></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=\lambda\underline{\boldsymbol{e}}\begin{pmatrix}{\lambda a_1c_1}\\{\lambda b_1^2}\\{b_1+c_1}\end{pmatrix}\neq \lambda G(\boldsymbol{u}).</center></math></div></td></tr>
</table>
Geoba