Question

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

Answer 1

A² = 9A + MI

⇒ A² - 9A = mI ….(1)

Now, A² = AA

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

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

Substituting A² in (1), we have

A² - 9A = mI

`=> [(4,0), (-9,49)]-9[(2,0), (-1,7)] =m[(1,0), (0,1)]`

`=> [(4,0), (-9,49)] - [(18,0), (-9,63)] = [(m,0), (0,m)]`

`=> [(-14,0), (0,-14)] = [(m,0), (0,m)]`

`=>` m = -14