Question

Find x, y, z, and w if `[(x - y, 2z + w),(2x - y, 2x + w)] = [(5, 3),(12, 15)]`.

Answer 1

Equate corresponding elements

x − y = 5   ...(i)

2z + w = 3   ...(ii)

2x − y = 12   ...(iii)

2x + w = 15   ...(iv)

To find x and y

Subtract equation (i) from (iii):

(2x − y) − (x − y) = 12 − 5

x = 7

Substitute x = 7 in equation (i):

7 − y = 5

−y = 5 − 7

−y = −2

y = 2

To find w

Substitute x = 7 in equation (iv):

2(7) + w = 15

14 + w = 15

w = 15 − 14

w = 1

To find z

Substitute w = 1 in equation (ii):

2z + 1 = 3

2z = 3 − 1

2z = 2

z = `2/2`

z = 1

Hence, x = 7, y = 2, z = 1, w = 1