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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 11 Maths Textbook Solution.

Answers (1)

Answer: x=11,y=9,z=3

Given: A=B

     \begin{bmatrix} x-2 & 3 &2z \\ 18z &y+2 & 6z \end{bmatrix} = \begin{bmatrix} y & z &6\\ 6y&x & 2y \end{bmatrix}

Hint: If A=B\Rightarrow    If two matrices are equal then the elements of each matrix are also equal.

Solution: Here A=B

           \begin{bmatrix} x-2 & 3 &2z \\ 18z &y+2 & 6z \end{bmatrix} = \begin{bmatrix} y & z &6\\ 6y&x & 2y \end{bmatrix}

Since corresponding entries of equal matrices are equal, So

x-2=y                                                                                                                                               ….. (i)

3=z                                                                                                                                                      ….. (ii)

2z=6                                                                                                                                                   ….. (iii)

18z=6y                                                                                                                                               ….. (iv)

y+2=x                                                                                                                                                ….. (v)

6z=2y                                                                                                                                                   ….. (vi)

Equation (ii) gives z=3

Putting the value of z in eqn(iv) we get

18\times 3=6y\\\Rightarrow y=9

Putting the value of  y  in eqn(v) we get

y+2=x\\\Rightarrow 9+2=x\\\Rightarrow x=11

Hence x=11,y=9,z=3

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