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Question
For the matrix A = `[(3,2),(1,1)]` find the numbers a and b such that A2 + aA + bI = O.
Solution
A2 + aA + bI = O
`= [(3,2),(1,1)] [(3,2),(1,1)] + "a" [(3,2),(1,1)] + "b" [(1,0),(0,1)] = [(0,0),(0,0)]`
`= [(9 + 2, 6 + 2),(3 + 1,2 + 1)] - [(3"a", 2"a"),("a","a")] + [("b",0),(0,"b")] = [(0,0),(0,0)]`
`= [(11 + 3"a" + "b", 8 + 2"a" + 0),(4 + "a" + 0, 3 + "a" + "b")] = [(0,0),(0,0)]`
4 + a = 0
a = -4
3 + a + b = 0
3 - 4 + b = 0
b = 1
`therefore` a = - 4, b = 1
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