91Ó°ÊÓ

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

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 $\left[\begin{array}{cc}2& 3\\ 5& 6\\ & \end{array}\right]$by 4 and second matrix $\left[\begin{array}{cc}-1& 7\\ 0& 4\\ & \end{array}\right]$by 2.

$\begin{array}{c}4A+2B−C=4\left[\begin{array}{cc}2& 3\\ 5& 6\end{array}\right]+2\left[\begin{array}{cc}−1& 7\\ 0& 4\end{array}\right]−\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]\\ =\left[\begin{array}{cc}4\left(2\right)& 4\left(3\right)\\ 4\left(5\right)& 4\left(6\right)\end{array}\right]+\left[\begin{array}{cc}2\left(−1\right)& 2\left(7\right)\\ 2\left(0\right)& 2\left(4\right)\end{array}\right]−\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]\\ =\left[\begin{array}{cc}8& 12\\ 20& 24\end{array}\right]+\left[\begin{array}{cc}−2& 14\\ 0& 8\end{array}\right]−\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]\end{array}$

Matrix addition/subtraction - 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.

$\begin{array}{c}4A+2B−C=\left[\begin{array}{cc}8& 12\\ 20& 24\end{array}\right]+\left[\begin{array}{cc}−2& 14\\ 0& 8\end{array}\right]−\left[\begin{array}{cc}9& −4\\ −6& 5\end{array}\right]\\ =\left[\begin{array}{cc}8−2−9& 12+14−\left(−4\right)\\ 20+0−\left(−6\right)& 24+8−5\end{array}\right]\\ =\left[\begin{array}{cc}−3& 30\\ 26& 27\end{array}\right]\end{array}$