00:01
Okay, so what we have here is a 3x5 matrix, wherein we are asked to find this raw echelon form and to determine its rank.
00:07
So if you are going to review our lessons, a matrix is in raw etcheron form if it satisfies the following conditions.
00:14
First, the first element in the first row should be a non -zero.
00:19
Second, each non -zero leading entry of the next row should be to the right of the leading entry in the previous row.
00:26
So it should resemble like this, like a staircase.
00:30
Finally, rows with all zero elements, if any, are below rows having a non -zero element.
00:36
So we can do this by performing a series of elementary row operations, including rescaling a row, adding a multiple of one row to the other row, and swapping the two rows.
00:48
So for this example, what we're going to do first is to cancel the leading coefficient of r2 by performing r2 minus one half of r1.
01:07
By doing that, we now have 2 -1 -3 -4 -2 -0 -negative 1 -half, 1 -5, and 2, 2 ,000.
01:32
Next, we want to cancel the leading coefficient of r3.
01:36
And we do this by subtracting r1, 2, r3.
01:45
With that, we now have 2, 1, 3 ,000, 3, 4, 2, 0, negative 1 1 1, 2, 1, 2, and 0.
02:01
2, negative 2, 1, and 5.
02:11
Next, we're going to swap r2 with r3...