#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 13 Maths Textbook Solution.

Answer: $x=1,y=2,z=4$ and $w=5$

Given: $\begin{bmatrix} x-y & z \\ 2x-y & w \end{bmatrix}$$= \begin{bmatrix} -1 &4\\ 0 & 5 \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: Here $\begin{bmatrix} x-y & z \\ 2x-y & w \end{bmatrix}$$= \begin{bmatrix} -1 &4\\ 0 & 5 \end{bmatrix}$

Since corresponding entries of equal matrices are equal, So

$x-y=-1$                                                                                                                                     ….. (i)

$z=4$                                                                                                                                            ….. (ii)

$2x-y=0$                                                                                                                                   ….. (iii)

$w=5$                                                                                                                                            ….. (iv)

Solving eqn(i) and (iii), we get

$\! \! \! \! \! \! x-y=-1\\2x-y=0\\-x=-1$

Putting the value of $x=1$ in eqn (i), we get

$1-y=-1\\\Rightarrow y=1+1\\\Rightarrow y=2$

Equation (ii) and (iv) gives the values of $z$ and $w$  respectively. So, $z=4,w=5$

Hence, $x=1,y=2,z=4$ and $w=5$