00:01
So we have a system of equations that we need to reduce down and that's jordan row reduce echelon form basically so we want to get some pivots and then we'll go ahead and figure out what our solution set will be free.
00:16
So we start out with the equations.
00:21
Negative 2 thirds x.
00:25
Plus y minus 1 third.
00:30
The.
00:32
Second equation is negative 1 third negative 2 thirds y and 1 z.
00:43
And the third equation is 1 x minus 1 third y minus 2.
00:51
The.
00:53
And this is all will be equal to basically the 0.
00:57
So what i've done is i've gone ahead and set up our augmented matrix.
01:03
So we can start doing row reduce echelon form.
01:05
The first step that we're going to do is multiply.
01:10
The 1st row by 3 halves negative 3 halves.
01:14
So that's going to give me.
01:16
Multiply by negative 3 halves.
01:18
1.
01:20
1 third.
01:22
And 1.
01:26
Negative 3, 2.
01:27
2 thirds and 1 third.
01:34
And we have 1 half.
01:37
1 and negative 2 thirds.
01:39
So you notice i've only changed the 1st row.
01:41
Nothing changes about.
01:44
The zeros.
01:47
Ok, so now what we do.
01:54
I'll write it here.
01:54
The next step.
01:56
We can take.
01:59
Row 2.
02:00
Add to it.
02:02
A third of row 1.
02:05
And so that will give us.
02:09
1 negative 3 halves.
02:12
1 half.
02:14
0.
02:16
Negative 7 6th.
02:17
And 7 6th.
02:19
And 1 negative 1 third.
02:23
Negative 2 thirds.
02:29
Alright, next step we need to take row 3.
02:34
And we will subtract row 1 from it.
02:42
Alright, so then that will give us.
02:46
1 negative 3 halves.
02:51
Positive 1 half.
02:54
0.
02:55
Negative 7 6th.
02:56
And 7 6th.
02:59
And 0.
03:01
So now we have a full pivot.
03:03
7 6th.
03:04
Negative 7 6th.
03:11
Ok, next thing.
03:13
So we have that.
03:14
Let's take the 2nd row.
03:16
And.
03:17
Multiply by.
03:20
6 7th.
03:22
Let's do negative 6 7th.
03:24
For the 2nd row.
03:30
And so that will give us.
03:33
1 negative 3 halves.
03:37
1 half.
03:40
0.
03:42
1 and negative 1.
03:45
And 0...