Question

Answer the following question:

Find matrices A and B, where 3A – B = `[(-1, 2, 1),(1, 0, 5)]` and A + 5B = `[(0, 0, 1),(-1, 0, 0)]`

Answer 1

Given equations are

3A – B = `[(-1, 2, 1),(1, 0, 5)]`   ...(i)

and A + 5B = `[(0, 0, 1),(-1,0, 0)]` ...(ii)

By (i) × 5 + (ii), we get

16A = `5[(-1, 2, 1),(1, 0, 5)] + [(0, 0, 1),(-1, 0, 0)]`

= `[(-5, 10, 5),(5, 0, 25)] + [(0, 0, 1),(-1, 0, 0)]`

∴ 16A = `[(-5, 10, 6),(4, 0, 25)]`

∴A = `1/16[(-5, 10, 6),(4, 0, 25)]`

By (i) – (ii) × 3, we get

–16B = `[(-1, 2, 1),(1, 0, 5)] -3[(0, 0, 1),(-1, 0, 0)]`

= `[(-1, 2, 1),(1, 0, 5)] - [(0, 0, 3),(-3, 0, 0)]`

∴ –16B = `[(-1, 2, -2),(4, 0, 5)]`

∴ B = `(-1)/16 [(-1, 2, -2),(4, 0, 5)]`

∴ B = `1/16 [(1, -2, 2),(-4, 0, -5)]`