Difference between revisions of "Selftest: Matrix multiplication with a scalar"

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{{ExerciseNavigation|previous=[[Selftest:Minors and cofactors|Minors and cofactors]]|chapter=[[Matrices]]|article=[[Multiplication with a scalar]]|next=[[Selftest:Transpose|Transpose]]}}
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{{ExerciseNavigation|previous=[[Selftest: Minors and cofactors|Minors and cofactors]]|chapter=[[Matrices]]|article=[[Multiplication with a scalar]]|next=[[Selftest: Transpose|Transpose]]}}
 
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{'''Fill in the correct values of the resulting matrix:'''<br/>
 
{'''Fill in the correct values of the resulting matrix:'''<br/>
 
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<math>\left[\begin{array}{ccc}3&0&1\\2&1&2\\0&3&1\end{array}\right]\cdot 3 =</math><br/>{ 9 } { 0 } { 3 }<br/>{ 6 } { 3 } { 6 }<br/>{ 0 } { 9 } { 3 }
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<math>\left[\begin{array}{ccc}3&2&1\\2&1&2\\2&3&1\end{array}\right]\cdot 3 =</math>
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<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/>
 
{'''Is the following equation correct?'''<br/>

Latest revision as of 10:23, 25 September 2014

← Previous exercise: Minors and cofactors Exercises for chapter Matrices | Article: Multiplication with a scalar Next exercise: Transpose →


1. Is there any scalar constant c, so that the following equation holds?

\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]
c=0.5
c=1
c=2
There is no c
→c=2 would be correct for all the green colored components in the result matrix: \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]. For the red component c=1.5 would be right. So there is no general c, that holds for all the components.

2. Is there any scalar constant c, so that the following equation holds?

\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]
c=0.5
c=1
c=2
There is no c
→If all the components of the left matrix are multiplied by c=2, it results in the right matrix.

3. Fill in the correct values of the resulting matrix:

\left[\begin{array}{ccc}3&2&1\\2&1&2\\2&3&1\end{array}\right]\cdot 3 =




4. Is the following equation correct?

\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]
Yes
No
→The central component in the resulting matrix is 2. But it has to be 3. So the equation is not correct.

5. Is the following equation correct?

\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]
Yes
No
→The multiplication holds for each of the components.

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