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.
+\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:
-\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))
\;\;\;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.
\;+\;\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.
