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Question
If `[(a, 1),(1, 0)] [(4, 3),(-3, 2)] = [(b, 11),(4, c)]` find a,b and c
Solution
`[(a, 1),(1, 0)] [(4, 3),(-3, 2)] = [(b, 11),(4, c)]`
⇒ `[(4a - 3, 3a + 2),(4 + 0, 3 + 0)] = [(b, 11),(4,c)]`
⇒ `[(4a - 3, 3a + 2),(4, 3)] = [(b, 11),(4,c)]`
Comparing the corresponding elements
3a + 2 = 11
⇒ 3a = 11 – 2 = 9
∴ a = `(9)/(3)` = 3
4a – 3 = b
⇒ b = 4 x 3 – 3
= 12 – 3
= 9
3 = c
Hence a = 3, b = 9, c = 3.
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