Q. 3 C5.0( 2 Votes )

# Show that each of the following systems of linear equations is consistent and also find their

Solutions :

5x + 3y + 7z = 4

3x + 26y + 2z = 9

7x + 2y + 10z = 5

Answer :

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:

(Adj A)x B≠0 or (Adj A)x B = 0

Cofactors of A are:

**C _{11}** = (– 1)

^{1 + 1}260 – 4 = 256

**C _{21}** = (– 1)

^{2 + 1}30 – 14 = – 16

**C _{31}** = (– 1)

^{3 + 1}6 – 182 = – 176

**C _{12}** = (– 1)

^{1 + 2}30 – 14 = – 16

**C _{22}** = (– 1)

^{2 + 1}50 – 49 = 1

**C _{32}** = (– 1)

^{3 + 1}10 – 21 = 11

**C _{13}** = (– 1)

^{1 + 2}6 – 182 = – 176

**C _{23}** = (– 1)

^{2 + 1}10 – 21 = 11

**C _{33}** = (– 1)

^{3 + 1}130 – 9 = 121

adj A =

=

Adj A x B =

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

Adj A =

Now, X = A ^{– 1}B =

=

=

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

Rate this question :

Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)

Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

RD Sharma - Volume 1Solve the following system of equations by matrix method:

2y – z = 1

x – y + z = 2

2x – y = 0

RD Sharma - Volume 1Find the adjoint of each of the following Matrices.

Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

RD Sharma - Volume 1Solve the following system of equations by matrix method:

3x + 7y = 4

x + 2y = – 1

RD Sharma - Volume 1Solve the following system of equations by matrix method:

x + y –z = 3

2x + 3y + z = 10

3x – y – 7z = 1

RD Sharma - Volume 1For the matrix A= , show that A(adj A)=O.

RD Sharma - Volume 1Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)

Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

RD Sharma - Volume 1If find and hence solve the system of equation

Mathematics - Board PapersIf , show that adj A=3A^{T}.