Posted by **Amy** on Saturday, March 24, 2012 at 5:22pm.

I don't quite understand how to solve matrices with three variables.

If I have the equations:

7x-4y-2z=0

2x-3y+z=-0.25

-2x-2y+5z=0

How can I solve this? I saw the explanation in a site but I didn't understand it. They appeared to make random operations until the matrix was:

1 0 0

0 1 0

0 0 1

I tried with the equations above but I got stuck no matter which order I had.

Please Help.

- Algebra -
**Damon**, Saturday, March 24, 2012 at 6:14pm
THAT IS CALLED GAUSS JORDAN REDUCTION

- Algebra -
**Damon**, Saturday, March 24, 2012 at 6:16pm
http://www.youtube.com/watch?v=JwT1FrLzEOQ

- Algebra -
**Damon**, Saturday, March 24, 2012 at 6:18pm
Here is a calculator

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

- Algebra -
**Damon**, Saturday, March 24, 2012 at 6:22pm
Step 2: Enter the values for your matrix, and press the "Solve" button.

7 -4 -2 0

2 -3 1 -1/4

-2 -2 5 0

Divide row1 by 7

1 -4/7 -2/7 0

2 -3 1 -1/4

-2 -2 5 0

Add (-2 * row1) to row2

1 -4/7 -2/7 0

0 -13/7 11/7 -1/4

-2 -2 5 0

Add (2 * row1) to row3

1 -4/7 -2/7 0

0 -13/7 11/7 -1/4

0 -22/7 31/7 0

Divide row2 by -13/7

1 -4/7 -2/7 0

0 1 -11/13 7/52

0 -22/7 31/7 0

Add (22/7 * row2) to row3

1 -4/7 -2/7 0

0 1 -11/13 7/52

0 0 23/13 11/26

Divide row3 by 23/13

1 -4/7 -2/7 0

0 1 -11/13 7/52

0 0 1 11/46

Add (11/13 * row3) to row2

1 -4/7 -2/7 0

0 1 0 31/92

0 0 1 11/46

Add (2/7 * row3) to row1

1 -4/7 0 11/161

0 1 0 31/92

0 0 1 11/46

Add (4/7 * row2) to row1

1 0 0 6/23

0 1 0 31/92

0 0 1 11/46

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