Question

Transform `[(1, -1, 2),(2, 1, 3),(3, 2, 4)]` into an upper traingular matrix by suitable row transformations.

Answer 1

Let A = `[(1, -1, 2),(2, 1, 3),(3, 2, 4)]` 

Applying R₂ → R₂ – 2R₁

and R₃ → R₃ – 3R₁, we get

`"A" ∼ [(1, -1, 2),(0, 3, -1),(0, 5, -2)]`

Applying `"R"_3 → "R"_3 - (5/3)"R"_2`, we get

`"A" ∼ [(1, -1, 2),(0, 3, -1),(0, 0, -(1)/(3))]`,

which is an upper triangular matrix.