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Thread: 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?

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

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

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

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

    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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