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

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

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Answer: x=3,y=7,z=-2,w=14

Given: \begin{bmatrix} x &3x-y \\ 2x+z & 3y-w \end{bmatrix}= \begin{bmatrix} 3 &2\\ 4 & 7 \end{bmatrix}

            We have to find the value of  x,y,z  and w

Hint: If two matrices are equal then the elements of each matrix are also equal.

Solution: Let \begin{bmatrix} x &3x-y \\ 2x+z & 3y-w \end{bmatrix}= \begin{bmatrix} 3 &2\\ 4 & 7 \end{bmatrix}

Since corresponding entries of equal matrices are equal, So

x=3                                                                                                                                                    ….. (i)

3x-y=2                                                                                                                                          ….. (ii)

2x+z=4                                                                                                                                         ….. (iii)

3y-w=7                                                                                                                                         ….. (iv)

Put the value of  x=3  in eqn(ii) we get

3\times 3-y=2\\\Rightarrow y=9-2\\\Rightarrow y=7

Put the value of  y=7  in eqn(iv) we get

3y-w=7\\\Rightarrow 3\times 7-w=7\\\Rightarrow w=21-7\\\Rightarrow w=14

Put the value of  x=3  in eqn(iii) we get

2x+z=4\\\Rightarrow 2\times 3+z=4\\\Rightarrow z=4-6\\\Rightarrow z=-2

Hence, x=3,y=7,z=-2,w=14

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