91Ó°ÊÓ

Matrix addition/subtraction and scalar multiplication:

If A and B are two matrices of order $m×n$, then the addition/subtraction of the two matrices will also yield a matrix of order $m×n$wherein each element is the sum/difference 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 $\left[\begin{array}{c}1\\ −1\\ −3\end{array}\right]$by 5, multiply each element in the second matrix $\left[\begin{array}{c}−4\\ 3\\ 5\end{array}\right]$by 6 and multiply each element in the third matrix $\left[\begin{array}{c}−3\\ 8\\ −4\end{array}\right]$by -2.

$\begin{array}{c}5\left[\begin{array}{c}1\\ −1\\ −3\end{array}\right]+6\left[\begin{array}{c}−4\\ 3\\ 5\end{array}\right]−2\left[\begin{array}{c}−3\\ 8\\ −4\end{array}\right]=\left[\begin{array}{c}5\left(1\right)\\ 5\left(−1\right)\\ 5\left(−3\right)\end{array}\right]+\left[\begin{array}{c}6\left(−4\right)\\ 6\left(3\right)\\ 6\left(5\right)\end{array}\right]+\left[\begin{array}{c}−2\left(−3\right)\\ −2\left(8\right)\\ −2\left(−4\right)\end{array}\right]\\ =\left[\begin{array}{c}5\\ −5\\ −15\end{array}\right]+\left[\begin{array}{c}−24\\ 18\\ 30\end{array}\right]+\left[\begin{array}{c}6\\ −16\\ 8\end{array}\right]\end{array}$

Add corresponding elements of both the matrices $\left[\begin{array}{c}5\\ −5\\ −15\end{array}\right]+\left[\begin{array}{c}−24\\ 18\\ 30\end{array}\right]+\left[\begin{array}{c}6\\ −16\\ 8\end{array}\right]$and simplify.

$\begin{array}{c}5\left[\begin{array}{c}1\\ −1\\ −3\end{array}\right]+6\left[\begin{array}{c}−4\\ 3\\ 5\end{array}\right]−2\left[\begin{array}{c}−3\\ 8\\ −4\end{array}\right]=\left[\begin{array}{c}5\\ −5\\ −15\end{array}\right]+\left[\begin{array}{c}−24\\ 18\\ 30\end{array}\right]+\left[\begin{array}{c}6\\ −16\\ 8\end{array}\right]\\ =\left[\begin{array}{c}5−24+6\\ −5+18−16\\ −15+30+8\end{array}\right]\\ =\left[\begin{array}{c}−13\\ −3\\ 23\end{array}\right]\end{array}$