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)]`

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

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

On comparing the coefficients of corresponding components,

2x + 3 = 9

⇒ x = 3

2y = 12

⇒ y = 6

and 2z – 3 = 15

⇒ z = 9

2t + 6 = 18

⇒ t = 6