00:01
In this video, we're going to find the general solution to the system of equations whose augmented matrix a is displayed here.
00:08
First, we need to row reduce this into row reduced echelon form, and so let's look to the pivots.
00:15
The first pivot is here, and we have zeros below, so we're all set on that position.
00:20
Next, we're going to pivot off this position here, which means we need to make this quantity equal to zero.
00:26
So our operation is going to be to replace row 1 with the quantity 3 times row 2 added to row 1.
00:37
When we do that, just imagine multiplying this entire row by 3, then adding the result to this row, and it will kill this coefficient here.
00:46
So after taking those operations, our matrix takes this new form that we see displayed here.
00:52
Next, we have a pivot here with zeros above and below.
00:55
After our last row operation, then this pivot position, there's zeros above and below, and the next pivot position is found by taking this, going down one row, and go right to the next non -zero entry.
01:09
So this is our next pivot position to work with.
01:12
We need to eliminate any quantity that's not zero above and below, so this quantity must be eliminated.
01:19
The row operation will take is replace row one with itself plus row three...