Question

# Solve begin{bmatrix}6 & -5&9 -4 & -5&3 end{bmatrix}=2X-5begin{bmatrix}2 & 1&-6 -6 & 6&3 end{bmatrix}

Matrices
Solve \begin{bmatrix}6 & -5&9 \\-4 & -5&3 \end{bmatrix}=2X-5\begin{bmatrix}2 & 1&-6 \\-6 & 6&3 \end{bmatrix}

2021-02-01

Step 1
Matrix addition and subtraction are same like adding and subtracting the given two numbers
Addition and subtraction is done with the same entries of the given two matrices
For example, if A and B are two matrices then addition is done as follows,
$$A=\begin{bmatrix}a & b \\c & d \end{bmatrix} \text{ and } B=\begin{bmatrix}e & f \\g & h \end{bmatrix}\text{Then } , A+B=\begin{bmatrix}a+e & b+f \\c+g & d+h \end{bmatrix}$$
Step 2
Now given,
$$\begin{bmatrix}6 & -5&9 \\-4 & -5&3 \end{bmatrix}=2X-5\begin{bmatrix}2 & 1&-6 \\-6 & 6&3 \end{bmatrix}$$

$$\begin{bmatrix}6 & -5&9 \\-4 & -5&3 \end{bmatrix}=2X-\begin{bmatrix}10 & 5&-30 \\-30 & 30&15 \end{bmatrix} 2X=\begin{bmatrix}6 & -5&9 \\-4 & -5&3 \end{bmatrix}+\begin{bmatrix}10 & 5&-30 \\-30 & 30&15 \end{bmatrix} 2X=\begin{bmatrix}16 & 0&-21 \\-34 & 25&18 \end{bmatrix} X=\frac{1}{2}\begin{bmatrix}16 & 0&-21 \\-34 & 25&18 \end{bmatrix}$$