Question

Apply the given elementary transformation on each of the following matrices `[(3, 1, -1),(1, 3, 1),(-1, 1, 3)]`, 3R₂ and C₂ ↔ C₂ – 4C₁.

Answer 1

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

Applying R₂ ↔ 3R₂ , we get

`"A" ∼ [(3, 1, -1),(3, 9, 3),(-1, 1, 3)]`

Applying C₂ → C₂ – 4C₁ on A, we get

`"A" ∼ [(3, 1 - 4(3), -1),(1, 3 - 4(1), 1),(-1, 1 - 4(-1), 3)]`

∴ `"A" ∼ [(3, 1 - 12, -1),(1, 3 - 4, 1),(-1, 1 + 4, 3)]`

∴ `"A" ∼ [(3, -11, -1),(1, -1, 1),(-1, 5, 3)]`.