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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, we get
2a + b = 2 ....(i)
3a – b = 3 ....(ii)
c + 2d = 4 ....(iii)
2c –d = – 1 ....(iv)
Adding (i) and (ii), we get
5a = 5
∴ a = 1
Substituting a = 1 in (i), we get
2(1) + b = 2
∴ b = 0
By (iii) + (iv) x 2, we get
5c = 2
∴ c = `(2)/(5)`
Substituting c = `(2)/(5)` i (iii), we get
`(2)/(5) + 2d` = 4
∴ 2d = `4 - (2)/(5)`
∴ 2d = `(18)/(5)`
∴ d = `(9)/(5)`.
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