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Question
Solve the following system of linear equations by matrix inversion method:
2x + 5y = – 2, x + 2y = – 3
Solution
`[(2, 5),(1, 2)][(x),(y)] = [(-2),(-3)]`
AX = B
X = `"A"^-1"B"`
∴ A = `[(2, 5),(1, 2)]`
|A| = 4 – 5
= – 1 ≠ 0,A–1 exists.
adj A = `[(2, -5),(-1, 2)]`
A–1 = `1/|"A"|`
adj A = `1/(-1) [(2, -5),(-1, 2)]`
= `[(-2, 5),(1, -2)]`
X = `"A"^-1"B"`
`[(x),(y)] = [(-2, 5),(1, -2)][(-2),(-3)]`
= `[(4 - 15),(-2 + 6)]`
`[(x),(y)] = [(-11),(4)]`
∴ x = –11, y = 4
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