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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 13 Maths Textbook Solution.

Answers (1)

Answer: x=1,y=2,z=4 and w=5

Given: \begin{bmatrix} x-y & z \\ 2x-y & w \end{bmatrix}= \begin{bmatrix} -1 &4\\ 0 & 5 \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: Here \begin{bmatrix} x-y & z \\ 2x-y & w \end{bmatrix}= \begin{bmatrix} -1 &4\\ 0 & 5 \end{bmatrix}

Since corresponding entries of equal matrices are equal, So

x-y=-1                                                                                                                                     ….. (i)

z=4                                                                                                                                            ….. (ii)

2x-y=0                                                                                                                                   ….. (iii)

w=5                                                                                                                                            ….. (iv)

Solving eqn(i) and (iii), we get

\! \! \! \! \! \! x-y=-1\\2x-y=0\\-x=-1

Putting the value of x=1 in eqn (i), we get

1-y=-1\\\Rightarrow y=1+1\\\Rightarrow y=2

Equation (ii) and (iv) gives the values of z and w  respectively. So, z=4,w=5

Hence, x=1,y=2,z=4 and w=5

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