00:03
Number 423, we want to solve this system of equations using the inverse matrix.
00:09
Okay, the first step is to write the matrix of coefficients.
00:15
So for the x's, we have 4, 2, and 0.
00:22
Okay, if one of the equations doesn't have an x, just put a zero for that variable.
00:30
Okay, for the ys, we have.
00:32
Negative 2, 2, and 6.
00:37
And for the zs, we have 3, negative 9, and negative 4.
00:46
On the right -hand side, we want to write the identity matrix, and we want to perform row operations until the identity matrix is on the left.
01:06
So first step, we want to get a 1 in the upper left.
01:09
I'm going to multiply row 1 times a fourth.
01:20
So we get 1 negative 2 4ths, 3 4ths, and 1 4th, 0.
01:41
Okay, recopy row rows 2 and 3.
01:46
All right.
01:55
And now we want to get zeros right here.
02:00
We're working one column at a time from left to right.
02:05
All right.
02:06
So we already have the zero in row three.
02:09
We want a zero right here.
02:11
I'm going to multiply row one times negative two and add it to row two.
02:22
So this is negative two, row one plus row two.
02:30
Okay, we're doing that with each element now.
02:36
So rewrite row one.
02:40
I'll reduce this fraction here.
02:44
That's a negative one -half.
02:53
Okay.
02:56
Now, negative two times one is negative two plus two is zero.
03:04
Okay? and you just keep doing that.
03:07
Negative two times negative two -fourths is going to be one plus two.
03:14
That's a three.
03:16
And keep going like that for each element.
03:48
Okay.
03:51
So the first column is, complete.
03:55
And now we want to have a one right here in place of the three.
04:00
So i'm going to multiply row two by a third.
04:31
Three times a third is one.
04:33
Negative 21 halves times a third is negative 21 over six and so on.
04:46
All right.
04:46
You can reduce the fractions now or later.
04:49
Sometimes i like to do them later.
04:59
Okay.
05:02
Now we want to get, we're working.
05:05
On the second column we want to get zeros in place of the six and the negative one half so i'm going to multiply row two times a half and add it to row one one half row two plus row one and i'm going to multiply row two times negative six and add it to row three negative six row two plus row three all right so times 0 plus 1 is just 1.
06:05
1 half times 1 plus negative 1 half is 0.
06:12
And just keep going like that for each element.
06:31
0 .1, i'm going to reduce this fraction to negative 7 halves.
06:38
This is negative 1, 6th, 1 3rd, and 0.
06:44
Lots of fractions.
06:45
I suggest you use a calculator that multiplies fractions.
06:51
Okay, and row three, negative six times row two plus row three.
06:57
So here we have a zero, negative six times one is negative six plus six is zero.
07:04
And keep going like that.
07:10
All right, and this is 17, one negative two and one...