Selftest: Multiplication of matrices

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Exercises for chapter Matrices | Article: Multiplication of matrices

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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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