Given A = [[2, 0], [-1, 7]] and I = [[1, 0], [0, 1]] and A² = 9A + mI. Find m.

Given:

A = [[2,0],[−1,7]] I = [[1,0],[0,1]]

A² = 9A + mI

First calculate A²:

A² = [[2,0],[−1,7]] [[2,0],[−1,7]]

= [[4,0],[−9,49]]

Now:

9A = [[18,0],[−9,63]]

Therefore:

mI = A² − 9A

= [[4,0],[−9,49]] − [[18,0],[−9,63]]

= [[−14,0],[0,−14]]

= −14I

Hence:

m = −14

Answer:

m = −14.

The complete matrix multiplication is shown before comparing the result with mI.