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Question
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
Solution
Given A = `[(3, 1),(-1, 2)]`
A2 = `[(3, 1),(-1, 2)] xx [(3, 1),(-1, 2)]`
= `[(9 - 1, 3 + 2),(-3 - 2, -1 + 4)]`
= `[(8, 5),(-5, 3)]`
L.H.S. = A2 – 5A + 7I2
= `[(8, 5),(-5, 3)] - 5[(3, 1),(-1, 2)] + 7[(1, 0),(0, 1)]`
= `[(8, 5),(-5, 3)] - [(15, 5),(-5, 10)] + [(7, 0),(0, 7)]`
= `[(-7, 0),(0, -7)] + [(7, 0),(0, 7)]`
= `[(0, 0),(0, 0)]`
= 0 = R.H.S.
L.H.S. = R.H.S.
∴ A2 – 5A + 7I2 = 0
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