How to find the determinant of this matrix?

Question

[ -1 5 9 -7 ]
[ 2 1 6 0 ]
[ 1 2 -4 8 ]

The question states tat I need to use gaussian elimination to calculate the determinant of the matrix.

This is what I get for the reduced matrx ( I cant seem to go any further )

[ 2 1 6 0 ]
[ 0 11/2 12 -7]
[ -3 0 -16 8 ]

Now how does this allow me to find the determinant more easily ? Thanks for your help

Answer 1

reduce the third line to start with a 0 using the first line. then make it's second value (still in the third row) be a zero using the second line. then divide the first line by 2 to reduce that etc.

i guess they think making more zeroes appear makes it easier to multiply out when u calculate the determinant. maybe when u finish reducing it u'll notice there's only a few numbers left.

Answer 2

If you use row transformations to convert the matrix to an upper triangular matrix, then the determinant is simply the product of the elements on the main diagonal.