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Question
Solve by matrix inversion method:
2x + 3y – 5 = 0; x – 2y + 1 = 0.
Solution
2x + 3y = 5
x – 2y = -1
The given system can be written as
`[(2,3),(1,-2)][(x),(y)] = [(5),(-1)]`
AX = B
where A = `[(2,3),(1,-2)]`, X = `[(x),(y)]` and B = `[(5),(-1)]`
|A| = `|(2,3),(1,-2)|` = - 4 - 3 = - 7 ≠ 0
∴ A-1 Exists.
adj A = `[(-2,-3),(-1,2)]`
`"A"^-1 = 1/|"A"|`(adj A)
= `1/(-7)[(-2,-3),(-1,2)]`
X = A-1B
`[(x),(y)] = -1/7[(-2,-3),(-1,2)][(5),(-1)]`
`=> -1/7[(-10+3),(-5-2)]`
`=> -1/7 [(-7),(-7)]`
`[(x),(y)] = [(1),(1)]`
∴ x = 1, y = 1
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