Question

Find matrix X, if AX = B, where A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "and B" = [(1),(2),(3)]`.

Answer 1

Given,AX = B

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

Applying R₂ → R₂ + R₃

`[(1, 2, 3),(0, 3, 6),(1, 2, 4)] "X" = [(1),(5),(3)]`

R₃ → R₃ – R₁, we get

`[(1, 2, 3),(0, 3, 6),(0, 0, 1)] "X" = [(1),(5),(2)]`

R₂ →`R_2/3`

`[(1, 2, 3),(0, 1, 2),(0, 0, 1)] "X" = [(1),(5/3),(2)]`

Applying R₂ → R₂ - 2R₃

`[(1, 2, 3),(0, 1, 0),(0, 0, 1)] "X" = [(1),(-7/3),(2)]`

R₁ → R₁ – 3R₃

`[(1, 2, 0),(0, 1, 0),(0, 0, 1)] "X" = [(-5),(-7/3),(2)]`

R₁ → R₁ – 2R₂

`[(1, 0, 0),(0, 1, 0),(0, 0, 1)] "X" = [(-1/3),(-7/3),(2)]`

IX = `[(-1/3),(-7/3),(2)]`

X = `[(-1/3),(-7/3),(2)]`