Question

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

Answer 1

A² = 9A + MI

`=>` A² – 9A =  MI  ...(1)

A² = AA

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

= `[((2xx2+0xx-1) (2xx0+0xx7)), ((-1xx2+7xx-1) (-1xx0+7xx7))]`

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

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

Substitute A² in (1)

A² – 9A = ml

`=> [(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

The value of m is –14.