00:01
All right, we're going to take a look at the following system of equations.
00:04
Take a look at our first equation.
00:06
We have an x2 plus 2x3 is equal to 3.
00:10
Now we don't have the x1.
00:15
So we want to put a 0 in for that one.
00:17
So we're going to have 0.
00:19
We're going to have a 1 and then a 2.
00:22
And then when it says equals 3, we're going to make a dash line going down and then put a 3.
00:28
All right.
00:29
For our next equation, we have a 3.
00:32
We have a 6 and we have a negative 2 and that's equal to negative 4 and then our last one we have a 2 and we do not have an x2 so we'll put a 0 and then we have a negative 6 and then a negative 8 okay so our augmented matrix is as follows so this is step number 1 and that is now done okay what we want to do next is we want to get to our re a reduced xxillin form of this.
01:07
Now, we have this, for the most part, set to go.
01:11
We have a zero here, and what we want to do is we want to be able to make a zero here and here instead.
01:20
So what i would like to do is we're going to switch row number one and row number three.
01:29
So let's go ahead.
01:31
Let's switch those.
01:32
So i have 2, 0, negative 6, and negative 8.
01:38
And then for row number 3, i'll have my 0, 1, 2, 3.
01:43
And my middle row has not changed.
01:46
That's still 3, 6, negative 2, negative 4.
01:52
Next up, we want to make this number into a 1.
01:56
And so to do that, we can divide everything by 2.
02:01
That's going to give me 1, 0 ,000, negative 3 and then negative 4.
02:13
Now nothing else has changed, so we're still going to have 3, 6, negative 2, negative 4, and then we'll have 0, 1, 2, and 3.
02:26
Okay, next thing we want to do is we want to make this 3 into a 0.
02:30
So to do that, we can do our first row times negative 3.
02:36
And i'll put those answers up here.
02:38
So this would be negative 3, this would be 0, this would be a positive 9, and this would be a positive 12.
02:46
And then what we want to do is we want to add that to row number two.
02:52
So let's go ahead...