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