Addition of matrices

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There are exercises as selftest for this article.

Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:

$\mathbf{A}+\mathbf{B}= \left[\begin{array}{cccc} a_{11} & a_{12} & \dots &a_{1n} \\ a_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1} & \dots & & a_{mn} \end{array}\right]+ \left[\begin{array}{cccc} b_{11} & b_{12} & \dots &b_{1n} \\ b_{21} &\ddots & &\vdots\\ \vdots & & & \\ b_{m1} & \dots & &b_{mn} \end{array}\right]= \left[\begin{array}{cccc} a_{11}+b_{11} & a_{12}+b_{12} & \dots &a_{1n}+b_{1n} \\ a_{21}+b_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} \end{array}\right]$

Example: Addition of two 3-by-3 matrices $\mathbf{A}_e+\mathbf{B}_e= \left[\begin{array}{ccc} 1 & 3 & -2\\ 0 & -1 & 3\\ 2 & 4 & 2 \end{array}\right]+ \left[\begin{array}{ccc} -3 & 2 & -1\\ 2 & 4 & -3\\ 0 & -2 & 1 \end{array}\right]= \left[\begin{array}{ccc} 1-3 & 3+2 & -2-1\\ 0+2 & -1+4 & 3-3\\ 2+0 & 4-2 & 2-1 \end{array}\right]= \left[\begin{array}{ccc} -2 & 5 & -3\\ 2 & 3 & 0\\ 2 & 2 & 1 \end{array}\right]$