Question

How do you find the determinant of `((5, 2, 0, 0, -2), (0, 1, 4, 3, 2), (0, 0, 2, 6, 3), (0, 0, 3, 4, 1), (0, 0, 0, 0, 2))`?

Answer 1

`-100`

Explanation:

The easiest way to calculate this determinant is by eliminating the number 3 in column 3 row 4.
This can be done by multiplying column 4 by `(-3/4)` and adding it to column 3 (remark that the value of the determinant remains the same)

`Det.=[[5,2,0,0,-2],[0,1,(4-3/4*3),3,2],[0,0,(2-3/4*6),6,3],[0,0,(3-3/cancel(4)*cancel(4)),4,1],[0,0,0,0,2]]`

`=[[5,2,0,0,-2],[0,1,7/4,3,2],[0,0,-5/2,6,3],[0,0,0,4,1],[0,0,0,0,2]]`

`= 5*1*(-5/cancel(2))*4*cancel(2)=-100`