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Math Help - Evaluating an equation in matrix form.

  1. #1
    Member MathBlaster47's Avatar
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    Evaluating an equation in matrix form.

    I'm not too sure what to do with this determinant, the question asks me to "solve the following equation.", but I don't understand what to do in order to achieve that.


    \begin{array}{|ccc|}0&0&-1\\3&x&0\\2&0&3\end{array}=x^2

    Do I just evaluate the determinant and work from there?

    Would (0\cdot x\cdot 3)+(2\cdot 0\cdot 0)+(3\cdot -1\cdot 0)-(2\cdot x\cdot -1)-(0\cdot 0\cdot 0)-(3\cdot 3\cdot 0)\rightarrow 0+0+0-(-2)x-0-0=-2x be a correct working for the question?
    Would that mean that x^2=-2x\therefore x=\{0,-2\}?

    Many thanks!
    Last edited by MathBlaster47; March 8th 2010 at 10:58 AM. Reason: changing title
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    I'm not too sure what to do with this determinant, the question asks me to "solve the following equation.", but I don't understand what to do in order to achieve that.


    \begin{array}{|ccc|}0&0&-1\\3&x&0\\2&0&3\end{array}=x^2

    Do I just evaluate the determinant and work from there?

    Would (0\cdot x\cdot 3)+(2\cdot 0\cdot 0)+(3\cdot -1\cdot 0)-(2\cdot x\cdot -1)-(0\cdot 0\cdot 0)-(3\cdot 3\cdot 0)\rightarrow 0+0+0-(-2)x-0-0=-2x be a correct working for the question?
    Would that mean that x^2=-2x\therefore x=\{0,-2\}?
    Mostly correct. The only mistake is that (2) = +2, so the equation should be x^2=2x
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  3. #3
    Member MathBlaster47's Avatar
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    Oops, well....one small slip in a generally correct answer isn't so bad!
    Thanks for your help!
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