Finding determinant by forward elimination

rebel girl 15

Use forward elimination to find the determinant of

1 0 1 -1
1 0 0 0
0 1 -1 -1
1 0 -1 0

My notes on this aren't great, but I was wondering if I am right in completing forward elimination, and then the determinant is +/- the product of the pivots if there is a pivot in every column, 0 otherwise, if during forward elimination I have to do an odd number of row swaps it is negative, positive if there are an even number of swaps

It just seemed too easy when I was doing it! I think I ended up with minus 1 as the answer

bnt

I know the procedure as "Gaussian Elimination"; assuming the matrix is invertible, and you do it right, you will end up with an upper-triangular matrix that looks something like:

D x x x
0 D x x
0 0 D x
0 0 0 D

where x is anything, and D is a diagonal term. The determinant is then the product of the diagonal terms.

I checked this matrix in Octave, and I also get a determinant of -1.

rebel girl 15

Cheers thanks for that!

LeixlipRed

You need to note as you've already sort of touched on that you need to correct the determinant by -1 for every row swap you complete and multiply by 1/k every time you multiply a row by k.

the_monkey

IS this college level maths ?

or is this on the LC now ?

been awhile since i was at school !

rebel girl 15

College - linear algebra module