00:01
Okay, so we have this system of equations for x, y and z, and we want to try and classify the solutions.
00:08
So let's write these in augmented matrix forms.
00:11
So the first equation here is going to give us minus 1, minus 1, minus 1, minus 6.
00:18
The second equation is 1, 1, 1, 0, and the final equation is 1, 1, minus 1, 4.
00:27
So we're going to change this as follows.
00:30
The first equation i'm just going to times everything by minus 1 to make everything positive so this first line is going to be 1 -1 -1 -6 the second equation i'm going to leave alone 1 -1 -0 and the third equation this line here i'm going to change by subtracting this line so this gives us 0 because we have 1 minus 1 second component in this line is 0 and finally we have minus 1 and which is minus 2, and then we have 4 minus 0, which is 4.
01:06
Okay, so we're at this point.
01:12
Finally, well, firstly, we can leave this top line alone, 1116.
01:19
I'm going to leave the second line alone for now, and then i'm going to times the final line by minus a half, so we get 0 ,0, 1, minus 2...