Question

Answer the following question:

Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`

Answer 1

Given equations are

2A – B = `[(1, -1),(0, 1)]`  ....(i)

and A + 3B = `[(1, -1),(0, 1)]`  ...(ii)

By (i) × 3 + (ii), we get

7A = `3[(1, -1),(0, 1)] + [(1, -1),(0, 1)]`

∴ 7A = `[(3, -3),(0, 3)] + [(1, -1),(0, 1)]`

∴ 7A = `[(4, -4),(0, 4)]`

∴ A = `1/7[(4, -4),(0, 4)]`

By (i) – (ii) × 2, we get

–7B = `[(1, -1),(0, 1)] -2[(1, -1),(0, 1)]`

= `[(1, -1),(0, 1)] - [(2, -2),(0, 2)]`

∴ –7B = `[(-1, 1),(0, -1)]`

∴ B = `- 1/7[(-1, 1),(0, -1)]`

∴ B = `1/7[(1, -1),(0, 1)]`