User:

To be able to add or subtract two matrices, they must be of the same size. Matrices of the same dimensions are added by adding corresponding elements.

$\fs2\left[\begin{array}a_{11}&a_{12}&\cdots&a_{1m}\\a_{21}&a_{22}&\cdots&a_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&a_{nm}\end{array}\right]+\left[\begin{array}b_{11}&b_{12}&\cdots&b_{1m}\\b_{21}&b_{22}&\cdots&b_{2m}\\\vdots&\vdots&\ddots&\vdots\\b_{n1}&b_{n2}&\cdots&b_{nm}\end{array}\right]=\left[\begin{array}a_{11}+b_{11}&a_{12}+b_{12}&\cdots&a_{1m}+b_{1m}\\a_{21}+b_{21}&a_{22}+b_{22}&\cdots&a_{2m}+b_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}+b_{n1}&a_{n2}+b_{n2}&\cdots&a_{nm}+b_{nm}\end{array}\right]$
Similarly, the subtraction of matrices can be done as shown:
$\fs2\left[\begin{array}a_{11}&a_{12}&\cdots&a_{1m}\\a_{21}&a_{22}&\cdots&a_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&a_{nm}\end{array}\right]-\left[\begin{array}b_{11}&b_{12}&\cdots&b_{1m}\\b_{21}&b_{22}&\cdots&b_{2m}\\\vdots&\vdots&\ddots&\vdots\\b_{n1}&b_{n2}&\cdots&b_{nm}\end{array}\right]=\left[\begin{array}a_{11}-b_{11}&a_{12}-b_{12}&\cdots&a_{1m}-b_{1m}\\a_{21}-b_{21}&a_{22}-b_{22}&\cdots&a_{2m}-b_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}-b_{n1}&a_{n2}-b_{n2}&\cdots&a_{nm}-b_{nm}\end{array}\right]$

$\left[\begin{matrix}2&-1&2\\0&-3&1\\4&0&1\end{matrix}\right]+\left[\begin{matrix}3&1&2\\0&2&-7\\0&0&-2\end{matrix}\right]=\left[\begin{matrix}5&0&4\\0&-1&-6\\4&0&-1\end{matrix}\right]$

$\left[\begin{matrix}2&-1&2\\0&-3&1\\4&0&1\end{matrix}\right]-\left[\begin{matrix}3&1&2\\0&2&-7\\0&0&-2\end{matrix}\right]=\left[\begin{matrix}-1&-2&0\\0&-5&8\\4&0&3\end{matrix}\right]$

$A=\left[\begin{matrix}0&1&4\\4&-2&7\\\end{matrix}\right]\;\;\;B=\left[\begin{matrix}3&2&4\\0&1&2\\\end{matrix}\right]\;\;\;C=\left[\begin{matrix}3&1\\6&4\\2&0\end{matrix}\right]$

Calculate A+B.

$A+B=\left[\begin{matrix}0&1&4\\4&-2&7\\\end{matrix}\right]\;+\;\left[\begin{matrix}3&2&4\\0&1&2\\\end{matrix}\right]\;=\left[\begin{matrix}3&-1&8\\4&-1&9\\\end{matrix}\right]$

Calculate A+C.
It is not possible to calculate A+C because they do not have the same dimensions.

Calculate:

 $\left[\begin{matrix}-2&5&1&0\\-2&-4&4&-3\\-1&-4&5&-5\\-4&2&-4&4\end{matrix}\right]+\left[\begin{matrix}1&-3&2&-3\\-4&-4&3&-5\\-2&3&1&1\\3&4&0&1\end{matrix}\right]=$