00:01
Okay, so we want to find the determinant of this matrix using gaussian elimination.
00:07
So we're going to transform this matrix into a diagonal matrix and we can use line switch and once it's a diagonal matrix we can find the determinant.
00:18
So since the first line is all one, we're going to subtract line one from each line.
00:29
So line 2 will be equal to line 2 minus line 1 light 3 will be equal to line 3 minus line 1 line 4 will be equal to 9 4 minus line 1 so line 1 remains unchanged line 2 will be 0 1 2 3 4 line 3 will be 0 0 2 2 0, 259, 14.
01:19
Line 4 will be 0, 3, 9.
01:27
20 minus 1 is 19.
01:32
And 35 minus 1 is 34.
01:37
9.
01:38
9 5 is 0 .4.
01:47
1434 and 69 okay now we're gonna have we're gonna remove the first so this is already starting to look like diagonal so we're gonna do line 3 equals to line 3 minus 2 line 2 line 2 line 4 equals to a line 4 equals to a line 4 equals to a line 4 minus 3 line 2 and 9 5 will be equal to line 5 minus 4 line 2.
02:36
So line 1 will remain unchanged.
02:41
Line 2 remains unchanged.
02:46
1, 2, 3, 4.
02:48
Now line 3, so 2 minus 2 is 0.
02:53
5 minus 4 is 1 9 minus 6 is 3 and 14 minus 8 is 6 3 minus 3 is 0 9 minus 6 is 10 19 minus 9 is 10 and 34 minus 9 minus 6 is 10 and 34 minus 12 is 22 and finally 0 minus 0 is 0 4 minus 4 is 0 14 minus 8 is 6 34 34 34 minus 12 is 22 and 69 minus 4 times uh 4 is 53 sorry about that.
04:20
Just want to make sure is, is it really 22? 34 minus three times four.
04:30
Yeah, yeah, it's really 22.
04:33
So now we continue.
04:37
We have two more lines here that don't really fit what we want...