#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 12 Maths Textbook Solution.

Answer: $x=3,y=7,z=-2,w=14$

Given: $\begin{bmatrix} x &3x-y \\ 2x+z & 3y-w \end{bmatrix}$$= \begin{bmatrix} 3 &2\\ 4 & 7 \end{bmatrix}$

We have to find the value of  $x,y,z$  and $w$

Hint: If two matrices are equal then the elements of each matrix are also equal.

Solution: Let $\begin{bmatrix} x &3x-y \\ 2x+z & 3y-w \end{bmatrix}$$= \begin{bmatrix} 3 &2\\ 4 & 7 \end{bmatrix}$

Since corresponding entries of equal matrices are equal, So

$x=3$                                                                                                                                                    ….. (i)

$3x-y=2$                                                                                                                                          ….. (ii)

$2x+z=4$                                                                                                                                         ….. (iii)

$3y-w=7$                                                                                                                                         ….. (iv)

Put the value of  $x=3$  in eqn(ii) we get

$3\times 3-y=2\\\Rightarrow y=9-2\\\Rightarrow y=7$

Put the value of  $y=7$  in eqn(iv) we get

$3y-w=7\\\Rightarrow 3\times 7-w=7\\\Rightarrow w=21-7\\\Rightarrow w=14$

Put the value of  $x=3$  in eqn(iii) we get

$2x+z=4\\\Rightarrow 2\times 3+z=4\\\Rightarrow z=4-6\\\Rightarrow z=-2$

Hence, $x=3,y=7,z=-2,w=14$