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Math Help - Solving for x in a matrix

  1. #1
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    Solving for x in a matrix

    Solve the following equation for x

    | x a x b |
    | b x a x | = 0
    | x b x a |
    | a x b x |

    (Determinant equals zero). I'm not sure how to do this and any help would be appreciated!
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  2. #2
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    Re: Solving for x in a matrix

    Quote Originally Posted by youngb11 View Post
    Solve the following equation for x

    | x a x b |
    | b x a x | = 0
    | x b x a |
    | a x b x |

    (Determinant equals zero). I'm not sure how to do this and any help would be appreciated!
    Do you know how to evaluate a 4x4 determinant?

    \displaystyle \begin{align*} \left|\begin{matrix} x & a & x & b \\ b & x & a & x \\ x & b & x & a \\ a & x & b & x \end{matrix}\right| &= x \left|\begin{matrix} x & a & x \\ b & x & a \\ x & b & x\end{matrix}\right| - a\left|  \begin{matrix} b & a & x \\ x & x & a \\ a & b & x \end{matrix}\right| + x\left|\begin{matrix} b & x & x \\ x & b & a \\ a & x & x \end{matrix}\right| - b\left|\begin{matrix} b & x & a \\ x & b & x \\ a & x & b \end{matrix}\right| \end{align*}

    Can you evaluate each of these 3 x 3 determinants?
    Thanks from youngb11
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  3. #3
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    Re: Solving for x in a matrix

    Before I continue with the rather length process, isn't there still the problem of 3 variables with only 1 equation?
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  4. #4
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    Re: Solving for x in a matrix

    Your answer will be in terms of a and b.

    You can reduce the work with some row operations.
    Thanks from youngb11
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