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Matrix Determinants

  1. Jul 7, 2010 #1
    1. The problem statement, all variables and given/known data
    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]


    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 [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?
     
  2. jcsd
  3. Jul 7, 2010 #2

    Mark44

    Staff: Mentor

    Check your arithmetic. I get 0 for both cofactors.
     
  4. Jul 7, 2010 #3
    The last line should be [1, -2, 2] instead of [-1, -2, 2]. That would make it 0
     
  5. Jul 7, 2010 #4
    Oh. haha you'd be right. Thanks!
     
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