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प्रश्न
Solve system of linear equations, using matrix method.
2x – y = –2
3x + 4y = 3
उत्तर
Given system of equations,
2x - y = - 2
3x + 4y = 3
The system of equations can be written as AX = B. Hence, x = A-1 B.
`A = [(2,-1),(3,4)], X = [(x),(y)] and B = [(-2),(3)]`
`=> abs A = [(2,-1),(3,4)] = 8 + 3 = 11 ne 0`
The cofactors of the elements of matrix A are as follows:
`A_11 = (-1)^(1 + 1) M_11 = 4, A_12 = (-1)^(1 + 2) M_12 = - 3`
`A_21 = (-1)^(2 + 1) M_21 = (-1)(-1) = 1,`
`A_22 = (-1)^(2 + 2) M_22 = (-1)^4 xx 2 = 2`
Matrix made of elements of cofactor of A = `[(4,-3),(1,2)]`
adj A `= [(4,-3),(1,2)] = [(4,1),(-3,2)]`
`A^-1 = 1/abs A (adj A) = 1/11 [(4,1),(-3,2)]`
`therefore X = A^-1 B = 1/11 [(4,1),(-3,2)] [(-2),(3)]`
`= 1/11 [(-8 + 3),(6 + 6)]`
`= 1/11 [(-5),(12)]`
`= [(-5/11),(12/11)]`
`=> [(x),(y)] = [(-5/11),(12/11)]`
`=> x = - 5/11 and y = 12/11`
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