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प्रश्न
Solve system of linear equations, using matrix method.
5x + 2y = 3
3x + 2y = 5
उत्तर
`[(5,2),(3,2)] [(x),(y)] = [(3),(5)] AX = "B"`
A = `[(5,2),(3,2)]`
`X = [(x),(y)] or B = [(3),(5)]`
Now, `abs A = [(5,2),(3,2)] = - 10 - 6 = 4 ne 0`
`=> A^-1` exists and hence the given equation has a minimal solution.
`therefore Adj A = [(2,-3),(-2,5)]^T = [(2,-2),(-3,5)]`
And `A^-1 = 1/abs A (Adj A)`
`= 1/4 [(2,-2),(-3,5)]`
`X = A^-1 B`
`=> [(x),(y)] = 1/4 [(2,-2),(-3,5)] [(3),(5)]`
`=> 1/4 [(6-4), (-9 + 25)]`
`=> 1/4[(-4), (16)]`
`= [(-1),(4)]`
x = -1, y = 4
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