Get Answers to all your Questions

header-bg qa

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

Answers (1)

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

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support