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Thread: Prove there always be a solution

  1. #1
    Oct 2009

    Prove there always be a solution

    The system
    has an obvious solution if [a b c] = [3 0 2]or[4 1 3]or[1 4 2]

    find these solutions.
    Prove or disprove: for any numbers $\displaystyle \alpha$, $\displaystyle \beta$, $\displaystyle \gamma$there is always a solution if
    [a b c] = $\displaystyle \alpha$[3 0 2] + $\displaystyle \beta$[4 1 3] + $\displaystyle \gamma$[1 4 2]

    Under what gerenal conditions on a,b,c will there always be a solution?

    the matrix [a b c] [3 0 2] [4 1 3] [1 4 2]supposed to be in column. I am kind of confused with the question

    I have solved the a part the 3 solution is $\displaystyle \left(\begin{array}{c}1 \\0 \\0\end{array}\right)$, $\displaystyle \left(\begin{array}{c}0 \\1 \\0\end{array}\right)$, and $\displaystyle \left(\begin{array}{c}-5 \\4 \\0\end{array}\right)$.

    now how do I prove there is always a solution under what condition
    Last edited by 450081592; Nov 15th 2009 at 04:41 PM.
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