Difference between revisions of "Selftest: Matrix multiplication with a scalar"
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− | {{ExerciseNavigation|previous=[[Selftest:Minors and cofactors|Minors and cofactors]]|article=[[ | + | {{ExerciseNavigation|previous=[[Selftest: Minors and cofactors|Minors and cofactors]]|chapter=[[Matrices]]|article=[[Multiplication with a scalar]]|next=[[Selftest: Transpose|Transpose]]}} |
+ | <br/> | ||
+ | |||
+ | <quiz display=simple> | ||
+ | {'''Is there any scalar constant <math>c</math>, so that the following equation holds?'''<br/> | ||
+ | :<math> | ||
+ | \left[\begin{array}{ccc}1&2&3\\0&2&1\\2&3&0\end{array}\right]\cdot c = \left[\begin{array}{ccc}2&4&6\\0&4&2\\3&6&0\end{array}\right] | ||
+ | </math><br/> | ||
+ | | typ="()" } | ||
+ | - <math>c=0.5</math> | ||
+ | - <math>c=1</math> | ||
+ | - <math>c=2</math> | ||
+ | + There is no <math>c</math> | ||
+ | ||<math>c=2</math> would be correct for all the green colored components in the result matrix: <math>\left[\begin{array}{ccc}{\color{Green}2}&{\color{Green}4}&{\color{Green}6}\\{\color{Green}0}&{\color{Green}4}&{\color{Green}2}\\{\color{Red}3}&{\color{Green}6}&{\color{Green}0}\end{array}\right]</math>. For the red component <math>c=1.5</math> would be right. So there is no general <math>c</math>, that holds for all the components. | ||
+ | |||
+ | {'''Is there any scalar constant <math>c</math>, so that the following equation holds?'''<br/> | ||
+ | :<math> | ||
+ | \left[\begin{array}{ccc}2&0&1\\0&2&3\\1&1&0\end{array}\right]\cdot c = \left[\begin{array}{ccc}4&0&2\\0&4&6\\2&2&0\end{array}\right] | ||
+ | </math><br/> | ||
+ | | typ="()" } | ||
+ | - <math>c=0.5</math> | ||
+ | - <math>c=1</math> | ||
+ | + <math>c=2</math> | ||
+ | - There is no <math>c</math> | ||
+ | ||If all the components of the left matrix are multiplied by <math>c=2</math>, it results in the right matrix. | ||
+ | |||
+ | {'''Fill in the correct values of the resulting matrix:'''<br/> | ||
+ | |typ="{}" } | ||
+ | <math>\left[\begin{array}{ccc}3&2&1\\2&1&2\\2&3&1\end{array}\right]\cdot 3 =</math> | ||
+ | <br/>{ 9 _2 } { 6 _2 } { 3 _2 }<br/>{ 6 _2 } { 3 _2 } { 6 _2 }<br/>{ 6 _2 } { 9 _2 } { 3 _2 } | ||
+ | |||
+ | {'''Is the following equation correct?'''<br/> | ||
+ | :<math>\left[\begin{array}{ccc}2&0&1\\4&1&3\\2&2&1\end{array}\right]\cdot 3 = \left[\begin{array}{ccc}6&0&3\\12&2&9\\6&6&3\end{array}\right]</math><br/> | ||
+ | | typ="()" } | ||
+ | - Yes | ||
+ | + No | ||
+ | ||The central component in the resulting matrix is <math>2</math>. But it has to be <math>3</math>. So the equation is not correct. | ||
+ | |||
+ | {'''Is the following equation correct?'''<br/> | ||
+ | :<math> | ||
+ | \left[\begin{array}{ccc}1&0&2\\2&1&3\\3&2&1\end{array}\right]\cdot 2 = \left[\begin{array}{ccc}2&0&4\\4&2&6\\6&4&2\end{array}\right] | ||
+ | </math><br/> | ||
+ | | typ="()" } | ||
+ | + Yes | ||
+ | - No | ||
+ | ||The multiplication holds for each of the components. | ||
+ | </quiz> |
Latest revision as of 10:23, 25 September 2014
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