If [(x-y, 2x+z), (2x-y, 3z+ω)] = [(-1, 5), (0, 13)] = [(-1, 5), (0, 13)], find x, y, z and w

Question

If \(\begin{bmatrix} x-y & 2x+z \\ 2x-y & 3z+ \omega \\ \end{bmatrix}=\) \(\begin{bmatrix} -1 & 5 \\ 0 & 13 \\ \end{bmatrix}=\) \(\begin{bmatrix} -1 & 5 \\ 0 & 13 \\ \end{bmatrix}\), find x, y, z and w

Answer 1

Given, matrix equation is:

\(\begin{bmatrix} x-y & 2x+z \\ 2x-y & 3z+ \omega \\ \end{bmatrix}=\) \(\begin{bmatrix} -1 & 5 \\ 0 & 13 \\ \end{bmatrix}\)

On equating the corresponding elements, we get

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

2x - y = 0 ....... (ii)

2x + z = 5 ...... (iii)

3z + w = 13 .......... (iv)

Subtracting eq. (ii), from (i), we get

Substituting x = 1 in eq. (i), we get

1 - y = - 1

⇒ - y = - 2

⇒ y = 2

Substituting the value of x in Eq. (iii), we get

2 × 1 + z = 5

⇒ z = 5 - 2 = 3

Substituting the value of z in Eq. (iv), we get

3 × 3 + w = 13

⇒ w = 13 - 9

w = 4

Thus, x = 1, y = 2, z = 3, w = 4