Difference between revisions of "Selftest: Multiplication of matrices"

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(Created page with "{{ExerciseNavigation|previous=Addition of matrices|chapter=Matrices|article=Multiplication of matrices|next=[[Selftest:Minors and cof...")
 
 
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{{ExerciseNavigation|previous=[[Selftest:Addition of matrices|Addition of matrices]]|chapter=[[Matrices]]|article=[[Multiplication of matrices]]|next=[[Selftest:Minors and cofactors|Minors and cofactors]]}}
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{{ExerciseNavigation|previous=[[Selftest: Addition of matrices|Addition of matrices]]|chapter=[[Matrices]]|article=[[Multiplication of matrices]]|next=[[Selftest: The determinant of a matrix|Determinant of a matrix]]}}
 
<br/>
 
<br/>
  
 
<quiz display=simple>
 
<quiz display=simple>
  
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{'''Fill in the correct values of the sum of the two matrices:'''<br/>
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{'''Consider the matrix multiplication <math>\mathbf{A}\cdot\mathbf{B}</math>. Which statement describes the requirements for this multiplication correctly?'''<br/>
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|typ="()" }
 +
- number of rows of <math>\mathbf{A}</math> has to equal number of colums of <math>\mathbf{B}</math>
 +
- number of rows of <math>\mathbf{A}</math> has to equal number of rows of <math>\mathbf{B}</math>
 +
+ number of colums of <math>\mathbf{A}</math> has to equal number of rows of <math>\mathbf{B}</math>
 +
- number of colums of <math>\mathbf{A}</math> has to equal number of colums of <math>\mathbf{B}</math>
 +
 
 +
{'''Which dimensions does the resulting matrix of a multiplication of an l-by-m with an m-by-n matrix have?'''<br/>
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|typ="()" }
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- m-by-m
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+ l-by-n
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- l-by-m
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- m-by-n
 +
 
 +
 
 +
{'''Mark the correct calculation specification for the following matrix multiplication:'''<br/>
 +
:<math> \left[\begin{array}{ccc}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\end{array}\right]\left[\begin{array}{cc}b_{11} & b_{12}\\ b_{21} & b_{22} \\ b_{31} & b_{32}\end{array}\right]=</math>
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|typ="()" }
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 +
- <math> \left[\begin{array}{ccc}a_{11}b_{11} & a_{12}b_{21} & a_{13}b_{31}\\a_{21}b_{12} & a_{22}b_{22} & a_{23}b_{32}\end{array}\right]</math>
 +
- <math> \left[\begin{array}{c}a_{11}b_{11} + a_{21}b_{12} \\ a_{12}b_{21} + a_{22}b_{22} \\ a_{13}b_{31} + a_{23}b_{32}\end{array}\right]</math>
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+ <math>\left[\begin{array}{cc}a_{11} b_{11}+a_{12} b_{21}+a_{13} b_{31} & a_{11} b_{12}+a_{12} b_{22}+a_{13} b_{12} \\a_{21} b_{11}+a_{22} b_{21}+a_{23} b_{31} & a_{21} b_{12}+a_{22} b_{22}+a_{23} b_{12}  \end{array}\right]</math>
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 +
{'''Which statements are correct?'''<br/>
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|typ="()" }
 +
- <math>\mathbf{A}\cdot\mathbf{B}=\mathbf{B}\cdot\mathbf{A}</math>
 +
+ <math>(\mathbf{A}\cdot\mathbf{B})\cdot\mathbf{C}=\mathbf{A}\cdot(\mathbf{B}\cdot\mathbf{C})</math>
 +
- <math>(\mathbf{A}+\mathbf{B})\cdot\mathbf{C}=\mathbf{A}+\mathbf{B}\cdot\mathbf{C}</math>
 +
- <math>\mathbf{A}\cdot(\mathbf{B}+\mathbf{C})\neq\mathbf{A}\cdot\mathbf{B}+\mathbf{A}\cdot\mathbf{C}</math>
 +
 
 +
{'''Solve the following multiplication:'''<br/>
 +
:<math> \left[\begin{array}{ccc}1&2&1\\3&1&2\end{array}\right]\left[\begin{array}{cccc}1&1&2&3\\2&1&3&1\\1&2&2&1\end{array}\right]=</math>
 +
|typ="{}" }
 +
{ 6 _3 } { 5 _3 } { 10 _3 } { 6 _3 }<br/>{ 7 _3 } { 8 _3 } { 13 _3 } { 12 _3 }
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 +
{'''Solve the following multiplication:'''<br/>
 +
:<math> \left[\begin{array}{ccc}1&3&2\end{array}\right]\left[\begin{array}{cc}2&1\\1&3\\4&1\end{array}\right]=</math>
 
|typ="{}" }
 
|typ="{}" }
−
<math>\left[\begin{array}{ccc}3&0&1\\2&1&2\\0&3&1\end{array}\right]+\left[\begin{array}{ccc}1&1&0\\0&3&1\\2&1&4\end{array}\right]=</math>
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{ 13 _3 } { 12 _3 }
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<br/>{ 4 _3 } { 1 _3 } { 1 _3 }<br/>{ 2 _3 } { 4 _3 } { 3 _3 }<br/>{ 2 _3 } { 4 _3 } { 5 _3 }
 
  
−
{'''Fill in the correct values of the sum of the two matrices:'''<br/>
+
{'''Solve the following multiplication:'''<br/>
 +
:<math> \left[\begin{array}{cc}1&2\\3&2\end{array}\right]\left[\begin{array}{cc}2&3\\1&2\end{array}\right]=</math>
 
|typ="{}" }
 
|typ="{}" }
−
<math>\left[\begin{array}{ccc}2&-2&3\\-1&3&1\\2&4&0\end{array}\right]+\left[\begin{array}{ccc}-1&3&-2\\0&2&1\\-1&2&1\end{array}\right]=</math>
+
{ 4 _3 } { 7 _3 } <br/> { 8 _3 } { 13 _3 }
−
<br/>{ 1 _3 } { 1 _3 } { 1 _3 }<br/>{ -1 _3 } { 5 _3 } { 2 _3 }<br/>{ 1 _3 } { 6 _3 } { 1 _3 }
 
  
 
</quiz>
 
</quiz>

Latest revision as of 10:22, 25 September 2014

← Previous exercise: Addition of matrices Exercises for chapter Matrices | Article: Multiplication of matrices Next exercise: Determinant of a matrix →


1. Consider the matrix multiplication \mathbf{A}\cdot\mathbf{B}. Which statement describes the requirements for this multiplication correctly?

number of rows of \mathbf{A} has to equal number of colums of \mathbf{B}
number of rows of \mathbf{A} has to equal number of rows of \mathbf{B}
number of colums of \mathbf{A} has to equal number of rows of \mathbf{B}
number of colums of \mathbf{A} has to equal number of colums of \mathbf{B}

2. Which dimensions does the resulting matrix of a multiplication of an l-by-m with an m-by-n matrix have?

m-by-m
l-by-n
l-by-m
m-by-n

3. Mark the correct calculation specification for the following matrix multiplication:

\left[\begin{array}{ccc}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\end{array}\right]\left[\begin{array}{cc}b_{11} & b_{12}\\ b_{21} & b_{22} \\ b_{31} & b_{32}\end{array}\right]=
\left[\begin{array}{ccc}a_{11}b_{11} & a_{12}b_{21} & a_{13}b_{31}\\a_{21}b_{12} & a_{22}b_{22} & a_{23}b_{32}\end{array}\right]
\left[\begin{array}{c}a_{11}b_{11} + a_{21}b_{12} \\ a_{12}b_{21} + a_{22}b_{22} \\ a_{13}b_{31} + a_{23}b_{32}\end{array}\right]
\left[\begin{array}{cc}a_{11} b_{11}+a_{12} b_{21}+a_{13} b_{31} & a_{11} b_{12}+a_{12} b_{22}+a_{13} b_{12} \\a_{21} b_{11}+a_{22} b_{21}+a_{23} b_{31} & a_{21} b_{12}+a_{22} b_{22}+a_{23} b_{12} \end{array}\right]

4. Which statements are correct?

\mathbf{A}\cdot\mathbf{B}=\mathbf{B}\cdot\mathbf{A}
(\mathbf{A}\cdot\mathbf{B})\cdot\mathbf{C}=\mathbf{A}\cdot(\mathbf{B}\cdot\mathbf{C})
(\mathbf{A}+\mathbf{B})\cdot\mathbf{C}=\mathbf{A}+\mathbf{B}\cdot\mathbf{C}
\mathbf{A}\cdot(\mathbf{B}+\mathbf{C})\neq\mathbf{A}\cdot\mathbf{B}+\mathbf{A}\cdot\mathbf{C}

5. Solve the following multiplication:

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


6. Solve the following multiplication:

\left[\begin{array}{ccc}1&3&2\end{array}\right]\left[\begin{array}{cc}2&1\\1&3\\4&1\end{array}\right]=

7. Solve the following multiplication:

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


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