91Ó°ÊÓ

Substitute$\left[\begin{array}{cc}−1& 7\\ 0& 4\end{array}\right]$ for B and$\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]$ for C into $3B-2C$.

$3B−2C=3\left[\begin{array}{cc}−1& 7\\ 0& 4\end{array}\right]−2\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]$

Scalar multiplication -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 of the first matrix $\left[\begin{array}{cc}−1& 7\\ 0& 4\end{array}\right]$by 3 and multiply each element of the second matrix $\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]$by 2.

$\begin{array}{c}3B−2C=3\left[\begin{array}{cc}−1& 7\\ 0& 4\end{array}\right]−2\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]\\ =\left[\begin{array}{cc}3\left(−1\right)& 3\left(7\right)\\ 3\left(0\right)& 3\left(4\right)\end{array}\right]−\left[\begin{array}{cc}2\left(9\right)& 2\left(−4\right)\\ 2\left(−6\right)& 2\left(5\right)\end{array}\right]\\ =\left[\begin{array}{cc}−3& 21\\ 0& 12\end{array}\right]−\left[\begin{array}{cc}18& −8\\ −12& 10\end{array}\right]\end{array}$

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

$\begin{array}{c}3B−2C=\left[\begin{array}{cc}−3& 21\\ 0& 12\end{array}\right]−\left[\begin{array}{cc}18& −8\\ −12& 10\end{array}\right]\\ =\left[\begin{array}{cc}−3−18& 21−\left(−8\right)\\ 0−\left(−12\right)& 12−10\end{array}\right]\\ =\left[\begin{array}{cc}−21& 29\\ 12& 2\end{array}\right]\end{array}$