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Pre-Calc

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I have to solve these using matrices by hand. Can someone please help me?

2x-3y-2z=4
(1/4)x-(2/5)y+(3/4)z=(-1/3)
-2x+1.3y-3z=5

Thank you so much! :)

  • Pre-Calc - ,

    2x-3y-2z=4
    (1/4)x-(2/5)y+(3/4)z=(-1/3)
    -2x+1.3y-3z=5
    ==============================
    Google Gauss Jordan reduction

    use all integers or fractions
    2 -3 -2 4
    1/4 -2/5 3/4 -1/3
    -2 13/10 -3 5


    Divide row 1 by 2
    1 -3/2 -1 2
    1/4 -2/5 3/4 -1/3
    -2 13/10 -3 5

    Add (-1/4 * row1) to row2
    1 -3/2 -1 2
    0 -1/40 1 -5/6
    -2 13/10 -3 5

    Add (2 * row1) to row3
    1 -3/2 -1 2
    0 -1/40 1 -5/6
    0 -17/10 -5 9

    Divide row2 by -1/40
    1 -3/2 -1 2
    0 1 -40 100/3
    0 -17/10 -5 9

    Add (17/10 * row2) to row3
    1 -3/2 -1 2
    0 1 -40 100/3
    0 0 -73 197/3

    Divide row3 by -73
    1 -3/2 -1 2
    0 1 -40 100/3
    0 0 1 -197/219

    Add (40 * row3) to row2
    1 -3/2 -1 2
    0 1 0 -580/219
    0 0 1 -197/219

    Add (1 * row3) to row1
    1 -3/2 0 241/219
    0 1 0 -580/219
    0 0 1 -197/219

    Add (3/2 * row2) to row1
    1 0 0 -629/219
    0 1 0 -580/219
    0 0 1 -197/219

  • Pre-Calc - ,

    I used this:
    http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

  • Pre-Calc - ,

    OMG thanks you so much!

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