SOLUTION: Solve the system using an augmented matrix. can you please shoe me the steps for doing this. thank you. 5x + 4y - z = 1 2x - 2y + z = 1 2x

SOLUTION: Solve the system using an augmented matrix. can you please shoe me the steps for doing this. thank you. 5x + 4y - z = 1 2x - 2y + z = 1 2x - y + z = 2

Question 176637: Solve the system using an augmented matrix. can you please shoe me the steps for doing this. thank you.
5x + 4y - z = 1
2x - 2y + z = 1
2x - y + z = 2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, pull out the coefficients and the right hand constants to form the augmented matrix:

Multiply Row 1 by to make the pivot 1:

Add -2*Row 1 to Row 2 to get the new Row 2

Add -2*Row 1 to Row 3 to get the new Row 3

Multiply Row 2 by to make the pivot 1:

Add 13/5*Row 2 to Row 3 to get the new Row 3

Multiply Row 3 by to make the pivot 1:

Add 7/18*Row 3 to Row 2 to replace Row 2

Add 1/5*Row 3 to Row 1 to replace Row 1

Add -4/5*Row 2 to Row 1 to replace Row 1

The matrix is now in reduced row echelon form

If you need more help with row reduction, check out the Linear Algebra Toolkit

Since the right hand column is , this means that , and
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