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Thread: Solutions of 3 x 3 matrix

  1. #1
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    Question Solutions of 3 x 3 matrix

    Hi,

    I hope someone can help (urgent).

    Let's suppose I have a system of three equations in three unknowns. Can such a system have exactly 2 distinct solutions?

    I would think that it is possible, but only in the event where the third unknown gets cancelled out during row reduction operations. I may be wrong however and would appreciate help on this!!!!

    - otownsend
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  2. #2
    MHF Contributor

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    Re: Solutions of 3 x 3 matrix

    NO, that is not possible! A system of any number of equations can have either one unique solution or an infinite number of solutions. In the case that you mention, "where the third unknown gets cancelled out during row reduction operations", you can have a unique solution for the other two unknowns but then the third can be any number- there are an infinite number of solutions.
    Last edited by HallsofIvy; Oct 6th 2017 at 10:33 AM.
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