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#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 20 Maths Textbook Solution.

Answer: $X = \begin{bmatrix} -2 &0 \\ -1 & -3 \end{bmatrix} and\: Y = \begin{bmatrix} 2& 1\\ 2 & 2 \end{bmatrix}$

Hint: Subtract matrix,$2X + 3Y and\: 3X + 2Y$. Then, solve.

Given:$2X + 3Y = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix} and\: 3X + 2Y = \begin{bmatrix} -2 &2 \\ 1 & -5 \end{bmatrix}$
Here, we have to compute x and y.
Solution:
$3 (2X + 3Y) - 2 (3X + 2Y) = 3 \begin{bmatrix} 2 & 3\\ 4& 0 \end{bmatrix} - 2 \begin{bmatrix} -2 &2 \\ 1&-5 \end{bmatrix}$

$6X + 9Y - 6X - 4Y =\begin{bmatrix} 6 &9 \\ 12 & 0 \end{bmatrix} - \begin{bmatrix} -4 & 4\\ 2& -10 \end{bmatrix}$

$5Y = \begin{bmatrix} 6+4 & 9-4\\ 12-2 & 0+10 \end{bmatrix}$

$5Y = \begin{bmatrix} 10 &5 \\ 10 & 10 \end{bmatrix}$

$Y = \begin{bmatrix} 2 &1\\ 2 & 2 \end{bmatrix}$
Also,
$2 (2X + 3Y) - 3 (3X + 2Y) = 2 \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix} - 3 \begin{bmatrix} -2 &2 \\ 1 & -5 \end{bmatrix}$

$4X + 6Y -9X-6Y =\begin{bmatrix} 4 &6 \\ 8 & 0 \end{bmatrix} - \begin{bmatrix} -6 &6 \\ 3 & -15 \end{bmatrix}$

$-5X = \begin{bmatrix} 4+6 &6-6 \\ 8-3 & 0+15 \end{bmatrix}$

$-5X = \begin{bmatrix} 10 &0 \\ 5 & 15 \end{bmatrix}$

$X = \begin{bmatrix} -2 &0 \\ -1& -3 \end{bmatrix}$