Question

On using elementary column operations C₂ → C₂ – 2C₁ in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: ______.

Options

• `[(1, -5),(0, 4)] = [(1, -5),(-2, 2)] [(3, -5),(2, 0)]`

• `[(1, -5),(0, 4)] = [(1, -1),(0, 1)] [(3, -5),(-0, 2)]`

• `[(1, -5),(2, 0)] = [(1, -3),(0, 1)] [(3, 1),(-2, 4)]`

• `[(1, -5),(2, 0)] = [(1, -1),(0, 1)] [(3, -5),(2, 0)]`

Answer 1

On using elementary column operations C₂ → C₂ – 2C₁ in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: `[(1, -5),(2, 0)] = [(1, -1),(0, 1)] [(3, -5),(2, 0)]`.

Explanation:

Given that, `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`

Using C₂ → C₂ – 2C₁, we get

`[(1, -5),(2, 0)] = [(1, -1),(0, 1)] [(3, -5),(2, 0)]`