#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 7 Maths Textbook Solution.

Answer: $X= \begin{bmatrix} 4 & 4\\ 0 & 4 \end{bmatrix} and \: Y=\begin{bmatrix} 1 &-2 \\ 0 & 5 \end{bmatrix}$
Hint: Try to add two matrices and find variable ‘X ’. Then substitute ‘X ’ value in any matrix to find ‘Y ’.

Given: $X + Y = \begin{bmatrix} 5 & 2\\ 0 & 9 \end{bmatrix} and\: X - Y = \begin{bmatrix} 3&6 \\ 0 & -1 \end{bmatrix}$
Here, we have to compute X  and Y.
Solution:

$\left ( X + Y \right )+\left ( X - Y \right ) = \begin{bmatrix} 5 & 2\\ 0 & 9 \end{bmatrix} + \begin{bmatrix} 3&6 \\ 0 & -1 \end{bmatrix}$

$\left ( X + Y \right )+\left ( X - Y \right ) = \begin{bmatrix} 5+3 & 2+6\\ 0+0 & 9-1 \end{bmatrix}$

$2X = \begin{bmatrix} 8 & 8\\ 0 & 8 \end{bmatrix}$

$X =\frac{1}{2} \begin{bmatrix} 8 & 8\\ 0 & 8 \end{bmatrix}$
$X = \begin{bmatrix} 4 & 4\\ 0 & 4 \end{bmatrix}$

Now,

$X+Y = \begin{bmatrix} 5 & 2\\ 0 & 9 \end{bmatrix}$

$\begin{bmatrix} 4 &4 \\ 0 & 4 \end{bmatrix}+Y = \begin{bmatrix} 5 & 2\\ 0 & 9 \end{bmatrix}$

$Y = \begin{bmatrix} 5 & 2\\ 0 & 9 \end{bmatrix}-\begin{bmatrix} 4 &4 \\ 0 & 4 \end{bmatrix}$

$Y = \begin{bmatrix} 1&- 2\\ 0 & 5 \end{bmatrix}$

$X= \begin{bmatrix} 4 & 4\\ 0 & 4 \end{bmatrix} and \: Y=\begin{bmatrix} 1 &-2 \\ 0 & 5 \end{bmatrix}$