Question

If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A^–1 = `1/k` (adj A), then k is ______.

Options

• 7

• – 7

• 15

• – 11

Answer 1

If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A^–1 = `1/k` (adj A), then k is 15.

Explanation:

If A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and

A^–1 = `1/k`adj (A)  ......(i)

Also we know A^–1 = `(adj(A))/|A|`  .......(ii)

∴ By comparing (i) and (ii)

|A| = k 

`\implies` |A| = `|(3, -2, 4),(1, 2, -1),(0, 1, 1)|`

= 3(2 + 1) + 2(1 + 0) + 4(1 – 0)

= 9 + 2 + 4

= 15