00:01
So the usefulness of the properties of determinants with respect to triangular matrices, we're asked to explain why that helps.
00:13
Okay? well, we can very quickly find the determinant of a matrix if it's triangular, which is why this property is very handy.
00:49
For instance, let's say i have a 3 by 3 matrix, 1, 2, 3, 4, 5, 6, so that it is triangular, right? and it's triangular because these entries are all zeros.
01:21
So it'll be triangular, i have to have zeros either all below or above the diagonal, the main diagonal.
01:27
Okay? so if i did the co -factor determinant on the first column, well, what happens? i have one times the determinant.
01:51
Take out the top row in the bottom and the left column.
01:54
And i'm left with the two by two, four, five, zero six.
01:59
And then zero times the next one and zero times the next one.
02:02
So those are gone.
02:04
Okay.
02:05
Well, one times anything is itself.
02:06
And the determinant of this 2 by 2 is 4 times 6 is 24 minus 0 is 24...