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Question
Solve system of linear equations, using matrix method.
5x + 2y = 4
7x + 3y = 5
Solution
The given equation,
5x + 2y = 4
7x + 3y = 5
`A = [(5,2),(7,3)], X = [(x),(y)] and B = [(4),(5)]`
`=> AX = B => X = A^-1 B`
The cofactors of the elements of matrix A are as follows
`A_11 = 3, A_12 = -7, A_21 = -2, A_22 = 5`
Matrix composed of the elements of the cofactor of A `= [(3,-7),(-2,5)]`
adj A = `[(3,-7),(-2,5)] = [(3,-2),(-7,5)]`
`abs A = abs ((5,2),(7,3)) = 15 - 14 = 1 ne 0`
`therefore A^-1 = 1/abs A (adj A)`
`= 1/1 [(3,-2),(-7,5)] = [(3,-2),(-7,5)]`
X = `A^-1 B = [(3,-2),(-7,5)][(4),(5)]`
`= [(12 - 10),(-28 + 25)] = [(2),(-3)]`
`=> [(x),(y)] = [(2),(-3)]`
=> x = 2 and y = -3
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