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.

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:

$\displaystyle \begin{vmatrix}3&1\\2&-1\end{vmatrix} = 3(-1) - (1)(2) = -3 - 2 = -5$

since i+j = 2+1 = 3, this gets multiplied by -1, so we get 5.

along the bottom row, 1st column:

$\displaystyle \begin{vmatrix}3&1\\1&1\end{vmatrix} = (3)(1) - (1)(1) = 3-1 = 2$

since i+j = 1+1 = 2, this stays as-is.

bottom row, 2nd column:

$\displaystyle \begin{vmatrix}1&1\\2&1\end{vmatrix} = (1)(1) - (1)(2) = 1-2 = -1$

since i+j = 3+2 = 5, this gets multiplied by -1, so it becomes 1.

bottom row, 3rd column:

$\displaystyle \begin{vmatrix}1&3\\2&1\end{vmatrix} = (1)(1) - (3)(2) = 1-6 = -5$

since i+j = 3+3 = 6, this stays as-is.

so i get what you say you're "supposed to get".