Question

If A = `[(5, 4),(-2, 3)]` and B = `[(-1, 3),(4, -1)]`, then find C^T, such that 3A – 2B + C = I, whre I is e unit matrix of order 2.

Answer 1

3A – 2B + C = I
∴ C = I + 2B – 3A

∴ C = `[(1, 0),(0, 1)] + 2[(-1, 3),(4, -1)] -3[(5, 4),(-2, 3)]`

∴ C = `[(1, 0),(0, 1)] +[(-2, 6),(8, -2)] - [(15, 12),(-6, 9)]`

∴ C = `[(1 - 2 - 15, 0 + 6 - 12),(0 + 8 + 6, 1 - 2 - 9)]`

∴ C = `[(-16, -6),(14, -10)]`

∴ C^T = `[(-16, 14),(-6, -10)]`