91Ó°ÊÓ

Matrix addition and scalar multiplication:

If A and B are two matrices of order $m×n$, then the addition of the two matrices will also yield a matrix of order $m×n$wherein each element is the sum of the corresponding elements.

The product of a scalar k and an $m×n$ matrix is an $m×n$ matrix in which each element equals k times the corresponding elements of the original matrix.

Multiply each element in the first matrix $\left[\begin{array}{ccc}\frac{1}{2}& 0& 1\\ 2& \frac{1}{3}& −1\end{array}\right]$by 5 and multiply each element in the second matrix $\left[\begin{array}{ccc}−2& \frac{3}{4}& 1\\ \frac{1}{6}& 0& \frac{5}{8}\end{array}\right]$by 4.

$\begin{array}{c}5\left[\begin{array}{ccc}\frac{1}{2}& 0& 1\\ 2& \frac{1}{3}& −1\end{array}\right]+4\left[\begin{array}{ccc}−2& \frac{3}{4}& 1\\ \frac{1}{6}& 0& \frac{5}{8}\end{array}\right]=\left[\begin{array}{ccc}5\left(\frac{1}{2}\right)& 5\left(0\right)& 5\left(1\right)\\ 5\left(2\right)& 5\left(\frac{1}{3}\right)& 5\left(−1\right)\end{array}\right]+\left[\begin{array}{ccc}4\left(−2\right)& 4\left(\frac{3}{4}\right)& 4\left(1\right)\\ 4\left(\frac{1}{6}\right)& 4\left(0\right)& 4\left(\frac{5}{8}\right)\end{array}\right]\\ =\left[\begin{array}{ccc}\frac{5}{2}& 0& 5\\ 10& \frac{5}{3}& −5\end{array}\right]+\left[\begin{array}{ccc}−8& 3& 4\\ \frac{2}{3}& 0& \frac{5}{2}\end{array}\right]\end{array}$

Add corresponding elements of both the matrices $\left[\begin{array}{ccc}\frac{5}{2}& 0& 5\\ 10& \frac{5}{3}& −5\end{array}\right]+\left[\begin{array}{ccc}−8& 3& 4\\ \frac{2}{3}& 0& \frac{5}{2}\end{array}\right]$and simplify.

$\begin{array}{c}5\left[\begin{array}{ccc}\frac{1}{2}& 0& 1\\ 2& \frac{1}{3}& −1\end{array}\right]+4\left[\begin{array}{ccc}−2& \frac{3}{4}& 1\\ \frac{1}{6}& 0& \frac{5}{8}\end{array}\right]=\left[\begin{array}{ccc}\frac{5}{2}& 0& 5\\ 10& \frac{5}{3}& −5\end{array}\right]+\left[\begin{array}{ccc}−8& 3& 4\\ \frac{2}{3}& 0& \frac{5}{2}\end{array}\right]\\ =\left[\begin{array}{ccc}\frac{5}{2}−8& 0+3& 5+4\\ 10+\frac{2}{3}& \frac{5}{3}+0& −5+\frac{5}{2}\end{array}\right]\\ =\left[\begin{array}{ccc}\frac{−11}{2}& 3& 9\\ \frac{32}{3}& \frac{5}{3}& −\frac{5}{2}\end{array}\right]\end{array}$