Q. 3 C5.0( 2 Votes )

# Show that each of the following systems of linear equations is consistent and also find theirSolutions :5x + 3y + 7z = 43x + 26y + 2z = 97x + 2y + 10z = 5

This can be written as:

|A| = 5(260 – 4) – 3(30 – 14) + 7(6 – 182)

= 5(256) – 3(16) + 7(176)

|A| = 0

So, A is singular. Thus, the given system is either inconsistent or it is consistent with infinitely many solution according to as:

Cofactors of A are:

C11 = (– 1)1 + 1 260 – 4 = 256

C21 = (– 1)2 + 1 30 – 14 = – 16

C31 = (– 1)3 + 1 6 – 182 = – 176

C12 = (– 1)1 + 2 30 – 14 = – 16

C22 = (– 1)2 + 1 50 – 49 = 1

C32 = (– 1)3 + 1 10 – 21 = 11

C13 = (– 1)1 + 2 6 – 182 = – 176

C23 = (– 1)2 + 1 10 – 21 = 11

C33 = (– 1)3 + 1 130 – 9 = 121

=

Now, AX = B has infinite many solution

Let z = k

Then, 5x + 3y = 4 – 7k

3x + 26y = 9 – 2k

This can be written as:

|A| = 121

Now, X = A – 1B =

=

=

There values of x,y,z satisfy the third equation

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