00:01
So suppose we have a system of linear equations that has a coefficient matrix.
00:05
I'm going to draw an example coefficient matrix having a pivot value in every row.
00:13
So these stars here are i guess weird triangle things just represent some non -zero values.
00:21
Or maybe they're even zero.
00:22
I don't know.
00:24
The point is we have a pivot position in every row.
00:29
This system is consistent because each individual equation is just a sum of a couple things that have to add up to, and this should be green, add up to zero or some other value.
00:41
In this case we have x1, 2, 3, 4.
00:46
X4 plus some value times x5 is equal to some value.
00:52
Right? excuse me.
00:54
And there like we can just fix x5 to be some unknown number.
01:00
X4 we can then solve for in terms of x5 as being something minus something times x5, whatever x5 is, and boom that's a solution...
