Question

If A = `[(1, 0),(1, 1)]`, B = `[(0, 1),(1, 0)]` and C = `[(1, 1),(0, 0)]`, the matrix A² + 2B – 3C is ______.

Options

• `[(-2, -1),(4, 1)]`

• `[(2, -1),(4, 1)]`

• `[(2, 1),(4, 1)]`

• `[(2, 1),(-4, -1)]`

Answer 1

If A = `[(1, 0),(1, 1)]`, B = `[(0, 1),(1, 0)]` and C = `[(1, 1),(0, 0)]`, the matrix A² + 2B – 3C is `underlinebb([(-2, -1),(4, 1)])`.

Explanation:

A² = A · A

= `[(1, 0),(1, 1)][(1, 0),(1, 1)]`

= `[(1, 0),(2, 1)]`

Now A² + 2B – 3C

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

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

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

= `[(-2, -1),(4, 1)]`