- #1
themadhatter1
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Homework Statement
Find the Determinant.
[tex]\left[\begin{array}{cccc}5&3&0&6\\4&6&4&12\\0&2&-3&4\\0&1&-2&2\end{array}\right][/tex]
Homework Equations
The Attempt at a Solution
I'm not sure why I can't get the determinant of this one right.
I chose to use the left most column to expand on because the two zeros make it easier
I have 2 cofactors since the other 2 would be multiplied by 0. The 4 is negative in [tex]C_{31}[/tex] because of the plus minus alternating pattern that is applied to the matrix.
[tex]C_{41}=5\left|\begin{array}{ccc}6&4&12\\2&-3&4\\-1&-2&2\end{array}\right|[/tex]
[tex]C_{31}=-4\left|\begin{array}{ccc}3&0&6\\2&-3&4\\1&-2&2\end{array}\right|[/tex]
[tex]C_{41}=5(-104)[/tex]
[tex]C_{31}=-4(0)[/tex]
If you add these you get -520, but the determinant of the 4x4 is 0. I also checked the determents of the smaller 3x3 cofactors and they are right. What am I doing wrong?