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Math Help - simple gauss elimination prob.

  1. #1
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    simple gauss elimination prob.

    For some reason I can't see how:
    x+3y-z = 1
    -4y + 5z = 4
    can become:
    x = 2-11t
    y =-1+5t
    z=4t

    Can someone explain the step/steps between?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by prime_66
    For some reason I can't see how:
    x+3y-z = 1
    -4y + 5z = 4
    can become:
    x = 2-11t
    y =-1+5t
    z=4t

    Can someone explain the step/steps between?

    x\ +\ 3y\ -\ z\ =\ 1
    -4y\ +\ 5z\ =\ 4

    is an under-determined system, so there will be
    a free parameter t in any solution. So we choose
    tso that it maximises the convenience of solving
    the system in terms of it.

    The constant on the RHS of the second equation is 4, as is the
    coefficient of y on the LHS. So setting z\ =\ 4t allows
    us to divide through by 4, and solve for y in terms of t.

    Having found y and z in terms of t
    we just substitute these into the first equation to solve for x
    in terms of t.

    RonL
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  3. #3
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    thanx, I thought z had to be equal to just t. but now i understand
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