Solve the following system of equations by matrix method:

5x + 2y = 3


3x + 2y = 5

The above system of equations can be written as


or AX = B


Where A = B = and X =


|A| = 10 – 6 = 4


So, the above system has a unique solution, given by


X = A – 1B


Let Cij be the cofactor of aijin A, then


C11 = (– 1)1 + 1 2 = 2


C12 = (– 1)1 + 2 3 = – 3


C21 = (– 1)2 + 1 2 = – 2


C22 = (– 1)2 + 2 2 = 5


Also, adj A =


=


A – 1 =


A – 1 =


Now, X = A – 1B






Hence, X = Y = 4


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