how do i solve this 4x4 determinant please help?

Question

[ -4, -5, -2, 2 ]
[ 1, 0, 0, 0 ]
[ 2, -1, 2, -5 ]
[ 4, 1, -4, -5 ]

Answer 1

The determinant of this huge thing is actually equal to the determinant of

(-1) [-5 -2 2]
[-1 2 -5]
[1 -4 -5]
Hope this helps

Answer 2

oprate from second row
-1 -5 -2 2
-1 2 -5
1 -4 -5
now solve like a 3 by 3 det.

Answer 3

Expand across the 2nd row, first. That will simplfy the problem to a single three by three which will be.

[5,2,-2]
[1,-2,5]
[-1,4,5]

Since you asked about a 4x4, I assume you know how to do a three by three. If you don't know how to expand across a row or column, see the link below