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.

Please Help.

  • Algebra -

    THAT IS CALLED GAUSS JORDAN REDUCTION

  • Algebra -

    http://www.youtube.com/watch?v=JwT1FrLzEOQ

  • 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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