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Question
If A = `[(2, 3),(1, 2)]` find x and y so that A² – xA + yI
Solution
Given
A2 = `[(2, 3),(1, 2)][(2, 3),(1, 2)]`
= `[(4 + 3, 6 + 6),(2 + 2, 3 +4)]`
= `[(7, 12),(4, 7)]`
∵ A2 = xA + yl
⇒ `[(7, 12),(4, 7)] = x[(2, 3),(1, 2)] + y[(1, 0),(0, 1)]`
⇒ `[(7, 12),(4, 7)] = [(2x, 3x),(x, 2x)] + [(y, 0),(0, y)]`
= `[(2x + y, 3x),(x, 2x + y)]`
Comparing the corresponding elements
3x = 12
⇒ x = 4
2x + y = 7
⇒ 2x 4 + y = 7
⇒ 8 + y = 7
⇒ y = 7 – 8 = –1
Hence x = 4, y = –1.
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