#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 8 Maths Textbook Solution.

Answer:  $a= 0,b=5,x=2$  and  $y= -1$
Given: Here given that

$\begin{bmatrix} 3x+4y & 2 &x-2y \\ a+b &2a-b & -1 \end{bmatrix}$  $= \begin{bmatrix} 2 & 2 &4\\ 5&-5 & -1 \end{bmatrix}$

We have to find the value of  $a,b,x$   and  $y$
Hint:  If two matrices are equal then the elements of each matrix are also equal.
Solution:  Given that two matrices are equal
$\therefore$  By equating them, we get
$3x+4y$                                                                                                                                       ……(i)
$x-2y$                                                                                                                                         ……(ii)
$a+b= 5$                                                                                                                                           ……. (iii)
$2a-b= -5$                                                                                                                                     …….. (iv)
Multiplying equation (ii) by 2 and adding to equation (i), we get
$\! \! \! \! \! \! \! \! 3x+4y+2x-4y= 2+8\\\Rightarrow 5x= 10\\\Rightarrow x= 2$
Now substituting the value of $x$ in eqn (i), we get
$3\times 2+4y= 2\\\Rightarrow 6 +4y= 2\\\Rightarrow 4y= -4\\\Rightarrow y= -1$
Now by adding eqn(iii) and eqn (iv)
$a+b+2a-b=5+\left ( -5 \right )$
$\Rightarrow 3a= 5-5$
$\Rightarrow a= 0$

Now, again substituting the value of $a$  in eqn(iii), we get
$a+b= 5$
$\Rightarrow b=5$

Hence, $a=0,b=5,x=2$  and  $y=-1$