#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 9 Maths Textbook Solution.

Answer:   $a= 3,b=5,x=2$  and $y=1$

Given:   $\begin{bmatrix} 2x-3y & a-b &3 \\ 1 &x+4y &3a+4b \end{bmatrix}$ $= \begin{bmatrix} 1 & -2 &3\\ 1&6 & 29 \end{bmatrix}$

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

$2x-3y=1$                                                                                                                                         ……. (i)

$x+4y=6$                                                                                                                                          ……. (ii)

$a-b=-2$                                                                                                                                          ……(iii)

$3a+4b= 29$                                                                                                                                      ……. (iv)

Multiplying eqn(ii) by 2 and subtracting from 2 we get

$\! \! \! \! \! \! 2x-3y-2x-8y= 1-12\\-11y= -11\\\Rightarrow y= 1$

Now, substituting the value of $y$  in equation (i) we get

$\! \! \! \! \! \! \! \! 2x-3\times 1= 1\\2x= 1+3\\2x= 4\\\Rightarrow x= 2$

Again, multiplying eqn(iii) by 4 and adding 4 we get

$\! \! \! \! \! \! \! 4a-4b+3a+4b=-8+29\\7a=21\\\Rightarrow a=3$

Substituting the value of $a$  in equation (iii)

$\! \! \! \! \! \! \! \! 3-b= -2\\\Rightarrow b=3+2\\\Rightarrow b=5$

Hence $a= 3,b=5,x=2$  and $y=1$