Question

Solve the equation for x, y, z and t, if `2[(x, z),(y, t)] + 3[(1, -1),(0, 2)] = 3[(3, 5),(4, 6)]`

Answer 1

`2[(x, z),(y, t)] + 3[(1, -1),(0, 2)] = 3[(3, 5),(4, 6)]`

⇒ `[(2x, 2z),(2y, 2t)] + [(3, -3),(0, 6)] = [(9, 15),(12, 18)]`

⇒ `[(2x + 3, 2z - 3), (2y, 2t + 6)] = [(9, 15), (12, 18)]`

Comparing the corresponding elements of these two matrices, we get:

2x + 3 = 9

⇒ 2x = 6

⇒ x = 3

2y = 12

⇒ y = 6

2z – 3 = 15

⇒ 2z = 18

⇒ z = 9

2t + 6 = 18

⇒ 2t = 12

⇒ t = 6

∴ x = 3, y = 6, z = 9 and t = 6