Alg 2 - Math

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need help with hw...

Use Gauss-Jordan to solve

3x – 2y + z = 6

3x + y – z = -4

-x + 2y – 2z = -8

  • Alg 2 - Math -

    Start by transcribing the equations to a 3x4 matrix
    3 -2 1 6
    3 1 -1 -4
    -1 2 -2 -8
    The first step is to reduce each column to zero (except the diagonal element and above) by linear combination of rows. I'll do the first one:
    3 -2 1 6
    0 3 -2 -10 (row 2 - row 1)
    0 4 -5 -18 (3*row 3 + row 1)
    Continue:
    3 -2 1 6
    0 3 -2 -10
    0 0 7 14 (4*row 2 - 3*row 3)
    The last row can be simplified:
    3 -2 1 6
    0 3 -2 -10
    0 0 1 2
    So z=2, substitute z=2 in row 2 to eliminate elements above the diagonal
    3 -2 0 4 (row 1 - row 3)
    0 3 0 -6 (row 2 + 2*row 3)
    0 0 1 2
    Simplify row 2:
    3 -2 0 4
    0 1 0 -2 (row 2/3)
    0 0 1 2
    Now eliminate column 2 from row 1
    3 0 0 0 (row 1 + 2*row 2)
    0 1 0 -2
    0 0 1 2
    So
    x=0
    y=-2
    z=2

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