Question

If A = `[(3, a),(-4, 8)]`, B = `[(c, 4),(-3, 0)]`, C = `[(-1, 4),(3, b)]` and 3A – 2C = 6B, find the values of a, b and c.

Answer 1

Given: A = `[(3, a),(-4, 8)]`, B = `[(c, 4),(-3, 0)]`, C = `[(-1, 4),(3, b)]`

∴ 3A = `3[(3, a),(-4, 8)] = [(9, 3a),(-12, 24)]`

6B = `6[(c, 4),(-3, 0)] = [(6c, 24),(-18, 0)]`

2C = `2[(-1, 4),(3, b)] = [(-2, 8),(6, 2b)]`

∵ 3A – 2C = 6B

∴ `[(9, 3a),(-12, 24)] - [(-2, 8),(6, 2b)] = [(6c, 24),(-18, 0)]`

`\implies [(9 - (-2), 3a - 8),(-12 - 6, 24 - 2b)] = [(6c, 24),(-18, 0)]`

`\implies [(11, 3a - 8),(-18, 24 - 2b)] = [(6c, 24),(-18, 0)]`

Comparing the corresponding terms, we have

3a – 8 = 24

`\implies` 3a = 24 + 8

`\implies` 3a = 32

`\implies a = 32/3 = 10 2/3`

And 24 – 2b = 0

`\implies` 2b = 24

`\implies` b = `24/2` = 12

And 6c = 11

`\implies c = 11/6 = 1 5/6`

Hence a = `10 2/3`, b = 12, c = `1 5/6`