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solve the system using gaussian elimination using the augmented matrix

0 votes
1  1  -5 3

1  0  -2 1

2 -1 -1  0
asked Jan 29, 2016 in ALGEBRA 1 by anonymous

1 Answer

0 votes

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 image and image.

Consider then

image

Substitute image and in image.

image

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

Solution:

Infinitely many solutions.

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

answered Jan 29, 2016 by cameron Mentor
edited Jan 29, 2016 by cameron

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