91Ó°ÊÓ

Matrix subtraction 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 $\left[\begin{array}{cc}2& 7\\ −3& 6\end{array}\right]$

by 4 and multiply each element in the second matrix$\left[\begin{array}{cc}−6& −4\\ 3& 0\end{array}\right]$

by 5.

$\begin{array}{c}4\left[\begin{array}{cc}2& 7\\ −3& 6\end{array}\right]+5\left[\begin{array}{cc}−6& −4\\ 3& 0\end{array}\right]=\left[\begin{array}{cc}4\left(2\right)& 4\left(7\right)\\ 4\left(−3\right)& 4\left(6\right)\end{array}\right]+\left[\begin{array}{cc}5\left(−6\right)& 5\left(−4\right)\\ 5\left(3\right)& 5\left(0\right)\end{array}\right]\\ =\left[\begin{array}{cc}8& 28\\ −12& 24\end{array}\right]+\left[\begin{array}{cc}−30& −20\\ 15& 0\end{array}\right]\end{array}$

Add corresponding elements of both the matrices $\left[\begin{array}{cc}8& 28\\ −12& 24\end{array}\right]+\left[\begin{array}{cc}−30& −20\\ 15& 0\end{array}\right]$and simplify.

$\begin{array}{c}4\left[\begin{array}{cc}2& 7\\ −3& 6\end{array}\right]+5\left[\begin{array}{cc}−6& −4\\ 3& 0\end{array}\right]=\left[\begin{array}{cc}8& 28\\ −12& 24\end{array}\right]+\left[\begin{array}{cc}−30& −20\\ 15& 0\end{array}\right]\\ =\left[\begin{array}{cc}8−30& 28−20\\ −12+15& 24+0\end{array}\right]\\ =\left[\begin{array}{cc}−22& 8\\ 3& 24\end{array}\right]\end{array}$