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 $\left[\begin{array}{cccc}0& −1& 7& 2\end{array}\right]$by 5 and multiply each element in the second matrix $\left[\begin{array}{cccc}5& −8& 10& −4\end{array}\right]$by 3.

$\begin{array}{c}5\left[\begin{array}{cccc}0& −1& 7& 2\end{array}\right]+3\left[\begin{array}{cccc}5& −8& 10& −4\end{array}\right]=\left[\begin{array}{cccc}5\left(0\right)& 5\left(−1\right)& 5\left(7\right)& 5\left(2\right)\end{array}\right]+\left[\begin{array}{cccc}3\left(5\right)& 3\left(−8\right)& 3\left(10\right)& 3\left(−4\right)\end{array}\right]\\ =\left[\begin{array}{cccc}0& −5& 35& 10\end{array}\right]+\left[\begin{array}{cccc}15& −24& 30& −12\end{array}\right]\end{array}$

Add corresponding elements of both the matrices $\left[\begin{array}{cccc}0& −5& 35& 10\end{array}\right]+\left[\begin{array}{cccc}15& −24& 30& −12\end{array}\right]$and simplify.

$\begin{array}{c}5\left[\begin{array}{cccc}0& −1& 7& 2\end{array}\right]+3\left[\begin{array}{cccc}5& −8& 10& −4\end{array}\right]=\left[\begin{array}{cccc}0& −5& 35& 10\end{array}\right]+\left[\begin{array}{cccc}15& −24& 30& −12\end{array}\right]\\ =\left[\begin{array}{cccc}0+15& −5−24& 35+30& 10−12\end{array}\right]\\ =\left[\begin{array}{cccc}15& −29& 65& −2\end{array}\right]\end{array}$