00:01
In this question, we are asked to write down an augmented matrix of the given system of equations and then reduce it to the row reduced echelon form and then determine the number of solutions.
00:12
And to create an augmented matrix, we simply need to write down the coefficients of the system of equations in front of x1, x2 and x3 and the right hand sides.
00:25
In the first line, there will be coefficients of the first equation, and the right hand side.
00:33
So it's going to be all ones.
00:35
In the second line, there will be coefficients of the second equation and the right hand side.
00:43
Then the third line consists of the coefficients of the third equation and the last line consists of the coefficients of the last equation.
00:53
And note that there is no x2 and basically it's equivalent to 0 to x2 being multiplied by 0.
01:01
So we'll replace its place by 0.
01:06
So this is an augmented matrix.
01:12
We will separate the right hand side by a vertical bar.
01:16
And now we need to reduce it to the row reduced echelon form.
01:21
To the row reduced echelon form.
01:24
There is only one row reduced echelon form.
01:29
So we'll start by, we want to get rid of these entries first.
01:37
And to do that, we will subtract the first row from the second row.
01:40
We will multiply the first row by 2 and add it to the third row.
01:47
And we will multiply it by negative 2, the 1 row by negative 2, and add it to the last row.
02:00
And here is what we are going to get.
02:03
We will rewrite the first row because it's not going to change.
02:09
So we are subtracting the first row from the second row.
02:13
1 minus 1 is 0.
02:18
Negative 1 minus 1 is negative 2.
02:23
1 minus 1 is 0.
02:28
2 minus 1 is 1.
02:31
In the third row, 1 times 2 minus 2 is going to be 0.
02:39
1 times 2 plus 2 is 4.
02:46
1 times 2 minus 2 is going to be 0.
02:53
1 times 2 minus 4.
02:55
2 minus 4 is negative 2.
02:59
Now let's move on to the last row.
03:02
1 times negative 2 plus 2 is going to be 0.
03:12
1 times negative 2 is negative 2 plus 0 is negative 2.
03:19
1 times negative 2 is negative 2 plus 2 is 0 and 1 times negative 2 is negative 2, negative 2 plus 3 is 1.
03:37
The next step would be to use this negative 2 to get rid of 4 and negative 2 below it.
03:48
And to do that, we need to multiply the 1st row by 2 and added to the 2 and added to the 3rd row.
03:56
And we need to subtract the second row from the last row.
04:07
Now i'm going to copy the matrix and then make the necessary adjustments...