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

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

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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}

                                                           

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