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Question
Solve system of linear equations, using matrix method.
4x – 3y = 3
3x – 5y = 7
Solution
`[(4,-3),(3,-5)] [(x),(y)] = [(3),(7)] AX = B`
A = `[(4,-3),(3,-5)]`
`X = [(x),(y)] and B = [(3),(7)]`
Now, `abs A = [(4,-3),(3,-5)] = - 20 + 9 = - 11 ne 0`
`=> A^-1` exists and hence the given equation has a unique solution.
`therefore Adj A = [(-5,-3),(3,4)]^T = [(-5,3),(-3,4)]`
and `A^-1 = 1/abs A (Adj A)`
`= 1/-11 [(-5,3),(-3,4)]`
`X = A^-1 B`
`=> [(x),(y)] = 1/11 [(-5,-3),(3,4)] [(3),(7)]`
` = [(-6/11),(-19/11)]`
So, x = `-6/11, y = -19/11`
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