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