#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 11 Maths Textbook Solution.

Answer: $x=11,y=9,z=3$

Given: $A=B$

$\begin{bmatrix} x-2 & 3 &2z \\ 18z &y+2 & 6z \end{bmatrix}$ $= \begin{bmatrix} y & z &6\\ 6y&x & 2y \end{bmatrix}$

Hint: If $A=B\Rightarrow$    If two matrices are equal then the elements of each matrix are also equal.

Solution: Here $A=B$

$\begin{bmatrix} x-2 & 3 &2z \\ 18z &y+2 & 6z \end{bmatrix}$ $= \begin{bmatrix} y & z &6\\ 6y&x & 2y \end{bmatrix}$

Since corresponding entries of equal matrices are equal, So

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

$3=z$                                                                                                                                                      ….. (ii)

$2z=6$                                                                                                                                                   ….. (iii)

$18z=6y$                                                                                                                                               ….. (iv)

$y+2=x$                                                                                                                                                ….. (v)

$6z=2y$                                                                                                                                                   ….. (vi)

Equation (ii) gives $z=3$

Putting the value of z in eqn(iv) we get

$18\times 3=6y\\\Rightarrow y=9$

Putting the value of  $y$  in eqn(v) we get

$y+2=x\\\Rightarrow 9+2=x\\\Rightarrow x=11$

Hence $x=11,y=9,z=3$