# Solve the following system of equations by matrix method:3x + y = 193x – y = 23

The above system of equations can be written as

or AX = B

Where A = B = and X =

|A| = – 3 – 3 = – 6

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 – 1 = – 1

C12 = (– 1)1 + 2 3 = – 3

C21 = (– 1)2 + 1 1 = – 1

C22 = (– 1)2 + 2 3 = 3

=

A – 1 =

A – 1 =

Now, X = A – 1B

Hence, X = 7 Y = – 2

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