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Math Help - Determinant of non square matrix

  1. #1
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    Determinant of non square matrix

    Heres the question:
    Determinant of non square matrix-stuck.gif

    I understand that the answer is |X'| multiplied by |X|. But how do you find the determinant of a non square matrix. I've heard a rumour that they cannot be defined or equal to zero.
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  2. #2
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     \left(\begin{array}{ccc}1 & 0 & 6 \\1 & 1 & 0\end{array}\right) \times \left(\begin{array}{cc}1 & 1 \\0 & 1 \\6 & 0\end{array}\right)= \left(\begin{array}{cc}37 & 1 \\1 & 2   \end{array}\right)

    \left | \begin{array}{cc}37 & 1 \\1 & 2   \end{array} \right | = 72
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  3. #3
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    Cheers for the help but I already knew what the multiple of X and X' was. What I want to know is the determinant of the two? Or do you simply find the determinant of the 3x3 matrix that results from multiplying them together? I was led to beleive that:
    |X'X| = |X'| x |X|
    and given that both X and X' are non square matrices how do you find their determianants?
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  4. #4
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    Quote Originally Posted by Brassy View Post
    Cheers for the help but I already knew what the multiple of X and X' was. What I want to know is the determinant of the two? Or do you simply find the determinant of the 3x3 matrix that results from multiplying them together? I was led to beleive that:
    |X'X| = |X'| x |X|
    and given that both X and X' are non square matrices how do you find their determianants?
    the result your trying to use is true for square matrices, I haven't studied matrices in great detail but form what I know it is not possible to find the determinate of a non-square matrix. I believe the question is suppose to be approached by the method I used in my pervious post.
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