Question

A = `[(2, 0),(-1, 7)], I = [(1, 0),(0, 1)]` and A² = 9A + kI, then the value of k is ______.

Options

• −14

• 14

• 12

• −12

Answer 1

A = `[(2, 0),(-1, 7)], I = [(1, 0),(0, 1)]` and A² = 9A + kI, then the value of k is −14.

Explanation:

A² = 9A + kI

A² = `[(2, 0),(-1, 7)] xx [(2, 0),(-1, 7)]`

= `[(2 xx 2 + 0 xx (-1), 2 xx 0 + 0 xx 7),((-1) xx 2 + 7 xx (-1), (-1) xx 0 + 7 xx 7)]`

= `[(4, 0),(-2 - 7, 49)]`

= `[(4, 0),(-9, 49)]`

9A = 9 `[(2, 0),(-1, 7)]`

= `[(18, 0),(-9, 63)]`

A² = 9A + kI

`[(4, 0),(-9, 49)] = [(18, 0),(-9, 63)] + k[(1, 0),(0, 1)]`

= `[(18 + k, 0),(-9, 63 + k)]`

Now compare element

18 + k = 4

k = 4 − 18

= −14