Question

Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.

Answer 1

AX = B

∴ `[(2, 1),(-1, 3)] X = [(12, -1),(1, 4)]`

Using : `R_1 -> R_1 + R_2`

`[(1, 4),(-1, 3)]X = [(13, 3),(1, 4)]`

Using : `R_2 -> R_2 + R_1`

`[(1, 4),(0, 7)]X = [(13, 3),(14, 7)]`

Using : `R_2 -> 1/7 R_2`

`[(1, 4),(0, 1)]X = [(13, 3),(2, 1)]`

Using : `R_1 -> R_1 - 4R_2`

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

∴ X = `[(5, -1),(2, 1)]`