Matrices

Addition and subtraction

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:

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



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