Question

Given, `A = [(3, 1), (5, 3)] and B = [(-1, a), (3, -5)]` and product AB = `[(b, 7), (4, 5)]`. Find the values of ‘a’ and ‘b’.

Answer 1

Given: A = `[(3, 1), (5, 3)]`

B = `[(-1, a), (3, -5)]`

AB = `[(b, 7), (4, 5)]`

⇒ AB = `[(3, 1), (5, 3)] xx [(-1, a), (3, -5)]`

⇒ AB = `[(3(-1) + 1(3)   3(a) + 1(-5)), (5(-1) + 3(3)   5(a) + 3(-5)) ]`

⇒ AB = `[(-3 + 3   3a - 5), (-5 + 9   5a - 15)]`

`[(b, 7), (4, 5)] = [(0   3a - 5), (4   5a - 15)]`

Comparing corresponding elements,

∴ b = 0

⇒ 3a − 5 = 7

⇒ 3a = 7 + 5

⇒ 3a = 12

⇒ a = `12/3`

⇒ a = 4

Hence, a = 4 and b = 0.