# Cofactor Expansion 4x4 linear algebra

Compute the determinant by cofactor expansions.

A=

   | 1 -2  5  2|
| 0  0  3  0|
| 2 -4 -3  5|
| 2  0  3  5|


I figured the easiest way to compute this problem would be to use a cofactor across row 2. So I got:

det A =

    |-1 -2  2|
-3| 2 -4  5|
| 2  0  5|


I went on to factor across the third row.

det A =

         ( |-2  2|    |-1 -2|)
-3(2|-4  5| + 5| 2 -4|)


det A = -3(2(-10+8)+5(4+4))

det A = -3(-4+40)

det A = -108

When I check my work on a determinate calculator I see that I should be getting det A = 12, but I can't seem to see where I'm messing up.

• You changed the sign of the upper left element: in your matrix it is $\;1\;$ , but then you changed it to $\;-1\;$ . Jun 25, 2016 at 23:07