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Question
If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.
Solution
`[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`
By equality of matrices,
2a + b = 2 ...(1)
3a – b = 3 ...(2)
c + 2d = 4 ...(3)
2c – d = – 1 ...(4)
Adding (1) and (2), we get,
5a = 5
∴ a = 1
∴ from (1), b = 2 – 2a = 2 – 2 = 0
Multiplying equation (3) by 2, we get,
2c + 4d = 8
Subtracting equation (4) from this equation, we get,
5d = 9
∴d = `9/5`
∴ from (3), `"c" + 2(9/5)` = 4
∴ c = `4 - 18/5 = 2/5`
Hence, a = 1 , b = 0, c = `2/5 and "d" = 9/5`.
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