SOLUTION: need to find the determinate of the following: please help! 3 0 -5 0 -5 1 1 2 2 7 1 0 -1 0 1 0 thx!

Question 443606: need to find the determinate of the following: please help!
3 0 -5 0
-5 1 1 2
2 7 1 0
-1 0 1 0
thx!
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
you have this matrix:

The only way to find the determinant is to use cofactor expansion.
Find the row or column with the most 0s or easy to work with numbers. I'm going to choose row 4.
Start with A[41].
It has a -1.
Cross out all values in row 4, and in column 1 to get this matrix:
=========================
Now find its determinant:
I assume you know how to find the determinant of a 3x3.
[0 + -70 + 0] - [0 + 0 + 0] = -70
So we have -1*-70 * (-1)^(1+4) = 70 * -1 = -70
So for cell[41] our cofactor is -70.
A[42] is 0
A[43] is 1
A[44] is 0
So focus on cell[43]
Cross out all values in row 4 and col 3.
To get this 3x3 matrix:
================
Again, find it's determinant: -42
So we have 1 * -42 * (-1)^(4+3) = -42 * -1 = 42
=======
To put it together take C41 + C43 to get -70 + 42 = -28
======
Our determinant of this 4x4 = -28

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