Question

If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.

Answer 1

AX = B

∴ `[(3, -1),(4, 2)] X = [(2),(-1)]`

By `R_2 → R_2 - R_1`

`[(3, -1),(1, 3)] X = [(2),(-3)]`

By `R_1 ↔ R_2`

`[(1, 3),(3, -1)] X = [(-3),(2)]`

By `R_2 -> R_2 - 3R_1`

`[(1, 3),(0, -10)] X = [(-3),(11)]`

By `R_2 → -1/10 R_2`

`[(1, 3),(0, 1)] X = [(-3),(-11/10)]`

By `R_1 → R_1 - 3R_2`

`[(1, 0),(0, 1)] X = [(3/10),(-11/10)]`

∴ X = `[(3/10),(-11/10)]`