themadhatter1
Jul7-10, 05:29 PM
1. The problem statement, all variables and given/known data
Find the Determinant.
\left[\begin{array}{cccc}5&3&0&6\\4&6&4&12\\0&2&-3&4\\0&1&-2&2\end{array}\right]
2. Relevant equations
3. The attempt at a solution
I'm not sure why I cant 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 C_{31} because of the plus minus alternating pattern that is applied to the matrix.
C_{41}=5\left|\begin{array}{ccc}6&4&12\\2&-3&4\\-1&-2&2\end{array}\right|
C_{31}=-4\left|\begin{array}{ccc}3&0&6\\2&-3&4\\1&-2&2\end{array}\right|
C_{41}=5(-104)
C_{31}=-4(0)
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?
Find the Determinant.
\left[\begin{array}{cccc}5&3&0&6\\4&6&4&12\\0&2&-3&4\\0&1&-2&2\end{array}\right]
2. Relevant equations
3. The attempt at a solution
I'm not sure why I cant 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 C_{31} because of the plus minus alternating pattern that is applied to the matrix.
C_{41}=5\left|\begin{array}{ccc}6&4&12\\2&-3&4\\-1&-2&2\end{array}\right|
C_{31}=-4\left|\begin{array}{ccc}3&0&6\\2&-3&4\\1&-2&2\end{array}\right|
C_{41}=5(-104)
C_{31}=-4(0)
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?