Q. 225.0( 2 Votes )

# Solve the following system of equations by matrix method:

3x + y = 19

3x – y = 23

Answer :

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 ^{– 1}B

Let C_{ij} be the cofactor of a_{ij}in A, then

C_{11} = (– 1)^{1 + 1} – 1 = – 1

C_{12} = (– 1)^{1 + 2} 3 = – 3

C_{21} = (– 1)^{2 + 1} 1 = – 1

C_{22} = (– 1)^{2 + 2} 3 = 3

Also, adj A =

=

A ^{– 1} =

A ^{– 1} =

Now, X = A ^{– 1}B

Hence, X = 7 Y = – 2

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