text: # Can't seem to calculate the right cofactors for this matrix
  
  • Oct 12th 2011, 10:40 PM
  CoryG89
  Can't seem to calculate the right cofactors for this matrix
  Not sure how to format a matrix properly on this forum. Someone feel free to let me know if you feel like it.
  
  The matrix A =
  
  1 3 1
  2 1 1
  -2 2 -1
  
  I keep getting -10 for the cofactor for the entry in the 2nd row 1st column,
  but it is actually 5.
  
  The last row I cannot get correct at all. I get -4, 2, and 5 for the cofactors on the 3rd row. But the correct ones are 2, 1, -5.
  
  I have no idea what I'm doing wrong, and it's weird as I feel like I have a pretty good understanding of the cofactors and I am able to calculate the rest of them.
  Any feedback would be appreciated. I have a test this morning.
  • Oct 13th 2011, 12:47 AM
  Deveno
  Re: Can't seem to calculate the right cofactors for this matrix
  well, without seeing your work, i don't know which step you're going wrong with.
  
  it's usually a matter of arithmetic, and you need to be really careful with your signs.
  
  if i delete the 2nd row, and first column, i get this:
  
  $\begin{vmatrix}3&1\\2&-1\end{vmatrix} = 3(-1) - (1)(2) = -3 - 2 = -5$
  
  since i+j = 2+1 = 3, this gets multiplied by -1, so we get 5.
  
  along the bottom row, 1st column:
  
  $\begin{vmatrix}3&1\\1&1\end{vmatrix} = (3)(1) - (1)(1) = 3-1 = 2$
  
  since i+j = 1+1 = 2, this stays as-is.
  
  bottom row, 2nd column:
  
  $\begin{vmatrix}1&1\\2&1\end{vmatrix} = (1)(1) - (1)(2) = 1-2 = -1$
  
  since i+j = 3+2 = 5, this gets multiplied by -1, so it becomes 1.
  
  bottom row, 3rd column:
  
  $\begin{vmatrix}1&3\\2&1\end{vmatrix} = (1)(1) - (3)(2) = 1-6 = -5$
  
  since i+j = 3+3 = 6, this stays as-is.
  
  so i get what you say you're "supposed to get".