Finding the Determinant of a matrix

[embury]

Hi, I have a 4x4 matrix and I need to determine the determinant for using cofactor expansion. I did that, but I used an online calculator to check my work and the determinant the calculator showed was different from the one I got. Since then I have done cofactor expansion using different rows and columns but I come up with a different answer each time. I'm obviously doing something wrong, but I can't figure it out. I'll post my work and if someone notices what I'm doing wrong could you please explain it to me. Thank you.

A=
-1 2 3 0
3 4 3 0
5 4 6 6
4 2 4 3
C34matrix=
-1 2 3
3 4 3
4 2 4
C44 matrix=
-1 2 3
3 4 3
5 4 6
Using cofactor expansion along column 4:
detA= 0C14 + 0C24 + 6C34 +3C44
detA= 6C34 +3C44
C34=(-1)^(3+4) *C34 matrix
=(-1)*(-1)*(16-6)
=10
C44=(-1)^(4+4)* C44 matrix
=(-1)*(24-12)
=-12

detA= 6C34 +3C44
detA= 6*10 + 3*(-12)
detA= 24

The online calculator says the determinant is 114, so what am I doing wrong? Am I missing a step or something?

[HallsofIvy]

"Using cofactor expansion along column 4:
detA= 0C14 + 0C24 + 6C34 +3C44
detA= 6C34 +3C44
C34=(-1)^(3+4) *C34 matrix
=(-1)*(-1)*(16-6)
=10"
How did you get that second -1? And how did you get 16-6? For C34, I get (-1)(-36)= 36, not 10.

I SUSPECT that you did only one term of the cofactor exapansion of C34 using the first column or first row.