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Math Help - Unique Solution

  1. #1
    Member
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    Singapore
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    Unique Solution

    Hi a short one, I got everything except this last part.

    Show that a unique solution exists for all other k. Find this solution.
    I constructed a matrix from the equations
    x+2y-2z = 5
    x-y+3z =-1
    x-7y+k = -k

    and found out that there will be infinite no of solutions when k =13
    When k is not 13, the system will have a unique solution, but as the question asks, how am I supposed to show? And how do I find the value when they say all other values of k, it doesn't make snese to e because I can't possibly use all values exceept 13..

    Thank you very much!
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  2. #2
    MHF Contributor
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    Re: Unique Solution

    Hey Tutu.

    Show that when k != 13 then the determinant of the matrix is non-zero and thus has an inverse (which means unique solution).

    Have you come across determinants?
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