Question

Solve the system of equations using matrices (row operations).If the system has no solution,say that it is inconsistent.

Answer 1

Step 1:

The system of equations is

Definition of augment matrix :

If  are the system of equations then the augmented matrix is .

Augment matrix of the system of equations is

Apply .

Apply .

Apply .

Step 2:

Number of variables .

Rank of the Matrix is 2.

Rank of the augmented matrix is 2.

Rank of = Rank of < , then the system has infinitely many solutions.

Solutions of the system of equations are

Consider , then

Substitute and in .

The solutions of the system of equations are .

Solution:

Infinitely many solutions.

The solutions of the system of equations are .