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

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

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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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