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Question
If A = `[(1, 4),(0, -1)], "B" = [(2, x),(0, -1/2)]`find the value of x if AB = BA
Solution
Given
A = `[(1, 4),(0, -1)][(2, x),(0, -1/2)]`
= `[(2 + 0, x - 2),(0 + 0, 0 + 1/2)]`
= `[(2, x - 2),(0, 1/2)]`
BA = `[(2, x),(0, -1/2)][(1, 4),(0, -1)]`
= `[(2 + 0, 8 - x),(0 + 0, 0 + 1/2)]`
= `[(2, 8 - x),(0, 1/2)]`
∵ AB = BA
∴ `[(2, x - 2),(0, 1/2)] = [(2, 8 - x),(0, 1/2)]`
Comparing the corresponding elements
x – 2 = 8 – x
⇒ x + x = 8 + 2
⇒ 2x = 10
∴ x = `(10)/(2)` = 5.
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