# Algebra

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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.

• Algebra -

THAT IS CALLED GAUSS JORDAN REDUCTION

• Algebra -

• Algebra -

Here is a calculator
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

• Algebra -

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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