# Determinant of non square matrix

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• Mar 20th 2008, 07:16 AM
Brassy
Determinant of non square matrix
Heres the question:
Attachment 5455

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.
• Mar 20th 2008, 07:27 AM
bobak
$\left(\begin{array}{ccc}1 & 0 & 6 \\1 & 1 & 0\end{array}\right) \times \left(\begin{array}{cc}1 & 1 \\0 & 1 \\6 & 0\end{array}\right)= \left(\begin{array}{cc}37 & 1 \\1 & 2 \end{array}\right)$

$\left | \begin{array}{cc}37 & 1 \\1 & 2 \end{array} \right | = 72$
• Mar 20th 2008, 07:32 AM
Brassy
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?
• Mar 20th 2008, 08:36 AM
bobak
Quote:

Originally Posted by Brassy
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.