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प्रश्न
For the matrix A = `[(3,2),(1,1)]` find the numbers a and b such that A2 + aA + bI = 0.
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उत्तर
We are given that A = `[(3,2),(1,1)]`
Now A2 + aA + bI = 0
`[(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)] + [(3a, 2a),(a,a)] + [(b,0),(0,b)] = [(0,0),(0,0)]`
⇒ `[(11 + 3a + b, 8 + 2a + 0),(4 + a + 0, 3 + a + b)] = [(0,0),(0,0)]`
⇒ 4 + a = 0
⇒ a = −4
Also, 3 + a + b = 0
⇒ 3 − 4 + b = 0
⇒ b = 1
∴ a = −4, b = 1
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