solve the system using gaussian elimination using the augmented matrix

Question

1  1  -5 3

1  0  -2 1

2 -1 -1  0

Answer 1

Step 1:

The augmented matrix is .

Augment matrix of the system of equations is .

Apply and .

Apply .

Apply .

Step 2:

Number of variables .

Rank of the Matrix is 3.

Rank of the augmented matrix is 2.

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

Solutions of system of equations are and .

Consider then

Substitute and in .

The solution of system is , where is any real number.

Solution:

Infinitely many solutions.

The solution of system is , where is any real number.