00:01
So of this system of two equations and two unknowns using the echelon method.
00:06
Okay, so i'm going to first set it up by creating this matrix where i'm focusing just on the coefficients of the equation.
00:15
On the left hand side of this straight line here, this kind of a section divider, i'm going to have the coefficients for the x and y.
00:25
So i have 7 and negative 6 from the top equation.
00:30
And then negative 14 and positive 12 from the bottom equation.
00:35
On the right hand side of that section divider, i'll have the negative 5 and then the 10.
00:43
Okay.
00:44
So the trick here is to try to get basically a bunch of zeros showing up so that hopefully maybe we'll have something that looks more like this.
00:55
1 -1 -0 and then numbers on the side over here.
01:02
And then over here.
01:04
So that's ideally what we're trying to do.
01:06
And we can do this by multiplying rows and then adding them to each other.
01:12
So those are basically the only two things we're allowed to do.
01:15
We can multiply and add or even subtract from each other.
01:19
Okay.
01:20
So looking at these two, what i notice is that seven is half of 14.
01:27
I also notice six is half of 12 and five is half of 10.
01:31
So something is really interesting going on here.
01:35
So let me play around with this a little bit.
01:38
Let's say we maybe multiply the top row.
01:42
So i'm going to call this row number one.
01:44
The top row will multiply it by two.
01:48
And then we'll add it to the second row.
01:51
So i'm going to make that my new, i'll write it down here, my new second row.
01:58
So that new second row will equal what it was plus.
02:04
Two times of the top one.
02:07
Just notes to myself here.
02:11
Okay, so the top row i'll keep it exactly like how it was.
02:16
And in my second row, okay, let's do this carefully.
02:20
I'll have negative 14 plus two times seven, which ends up being a 14 plus positive 14, which is zero.
02:30
So i'll put a zero there.
02:32
For the middle one, i'll have 12, which is what it was originally, plus two times what was above it.
02:42
So i'll have 12 plus negative 12, which is zero.
02:46
Oh, very interesting, which is zero showing up.
02:50
And then for the last spot, i'll have what it was originally, 10 plus two times what it was above it.
02:57
So negative 5, 10 plus negative 10 equals 0.
03:02
Okay, so i have a bunch of zeros showing up...