Question

# If 3begin{bmatrix}x_1 & x_2 x_3 & x_4 end{bmatrix}=begin{bmatrix}x_1 & 2 -1 & 4x_4 end{bmatrix}+begin{bmatrix}4 & x_1+x_2 x_3+x_4 & 3 end{bmatrix} 1.

Matrices
If $$3\begin{bmatrix}x_1 & x_2 \\x_3 & x_4 \end{bmatrix}=\begin{bmatrix}x_1 & 2 \\-1 & 4x_4 \end{bmatrix}+\begin{bmatrix}4 & x_1+x_2 \\x_3+x_4 & 3 \end{bmatrix}$$
1. $$x_1=-2 , x_2=2 , x_3=-2 , x_4=-3$$
2. $$x_1=2 , x_2=-2 , x_3=-2 , x_4=-3$$
3. $$x_1=2 , x_2=2 , x_3=2 , x_4=-3$$
4. $$x_1=2 , x_2=2 , x_3=-2 , x_4=3$$
5, $$x_1=2 , x_2=2 , x_3=-2 , x_4=-3$$

2021-02-17
Step 1
We will perform the addition and scalar multiplication of matrices on both the sides.
Then we will compare corresponding elements in both matrices and will solve the equations.
Step 2
$$3\begin{bmatrix}x_1 & x_2 \\x_3 & x_4 \end{bmatrix}=\begin{bmatrix}x_1 & 2 \\-1 & 4x_4 \end{bmatrix}+\begin{bmatrix}3 & x_1+x_2 \\x_3+x_4 & 3 \end{bmatrix}$$
$$\therefore \begin{bmatrix}3x_1 & 3x_2 \\3x_3 & 3x_4 \end{bmatrix}=\begin{bmatrix}x_1+4 & 2+x_1+x_2 \\x_3+x_4-1 & 4x_4+3 \end{bmatrix}$$
$$\therefore 3x_1=x_1+4$$
$$2x_1=4$$
$$x_1=2$$
$$\therefore 3x_4=4x_4+3$$
$$x_4+3=0$$
$$x_4=-3$$
$$\therefore 3x_2=2+x_1+x_2$$
$$2x_2=2+x_1$$
$$2x_2=2+2$$
$$x_2=2$$
$$\therefore 3x_3=x_3+x_4-1$$
$$2x_3=x_4-1$$
$$=-3-1$$
$$x_3=-2$$
$$\therefore x_1=2,x_2=2,x_3=-2,x_4=-3$$
option 5