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Question
Solve the following system of linear equations by matrix inversion method:
2x – y = 8, 3x + 2y = – 2
Solution
`[(2, -1),(3, 2)][(x),(y)] = [(8),(-2)]`
AX = B
X = `"A"^-1"B"`
A = `[(2, -1),(3, 2)]`
|A| = 4 + 3
= 7 ≠ 0.A−1 exists.
adj A = `[(2, 1),(-3, 2)]`
A−1 = `1/|"A"|` adj A
A−1 = `1/7[(2, 1),(-3, 2)]`
X = `"A"^-1"B"`
X = `1/7 [(2, 1),(-3, 2)][(8),(-2)]`
`[(x),(y)] = 1/7[(16 - 2),(-24 - 4)]`
`[(x),(y)] = 1/7[(14),(-28)]`
= `[(2),(-4)]`
x = 2, y = – 4
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