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Question
Find a and b if `[(a - b, b - 4),(b + 4, a - 2)] [(2, 0),(0, 2)] = [(2, -2),(14, 0)]`
Solution
Given
`[(a - b, b - 4),(b + 4, a - 2)] [(2, 0),(0, 2)] = [(2, -2),(14, 0)]`
⇒ `[(2a - 2b + 0, 0 + 2a - 2b),(2b + 8 + 0, 0 + 2a - 4)] = [(-2, -2),(14, 0)]`
⇒ `[(2a - 2b, 2a - 2b),(2b + 8, 2a - 4)] = [(-2, -2),(14, 0)]`
Comparing the corresponding elements
2a – 4 = 0
⇒ 2a = 4
⇒ a = 2
2a – 2b = –2
⇒ 2 x 2 – 2b = –2
⇒ 4 – 2b = –2
⇒ –2b = –2 – 4 = –6
⇒ b = 3
Hence a = 2, b = 3.
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