Question

The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is ______.

Options

• `-1/3[(-3, 0, 0),(3, 1, 0),(9, 2, -3)]`

• `-1/3[(-3, 0, 0),(3, -1, 0),(-9, -2, 3)]`

• `-1/3[(3, 0, 0),(3, -1, 0),(-9, -2, 3)]`

• `-1/3[(-3, 0, 0),(-3, -1, 0),(-9, -2, 3)]`

Answer 1

The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is `underlinebb(-1/3[(-3, 0, 0),(3, -1, 0),(-9, -2, 3)]`.

Explanation:

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

So, |A| = `|(1, 0, 0),(3, 3, 0),(5, 2, -1)|`

= 1(3 × (–1) – 0) – 0(3 × (–1) – 0 – 0) + 0(3 × 2 – 5 × 3)

= 1 × (–3) – 0 – 0

= – 3

Now, adj A

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

= `[(-3, 3, -9),(0, -1, -2),(0, 0, 3)]`

adj A = `[(-3, 0, 0),(3, -1, 0),(-9, -2, 3)]`

Hence, A^–1 = `1/|A|` adj A = `1/(-3)|(-3, 0, 0),(0, -1, 0),(-9, -2, 3)|`