00:01
Show whether b is in the column space of a, all we need to do is show that ax equals b has a consistent solution.
00:06
So to do that, i put an augmented matrix here with a and b, and we're going to do gauzing elimination.
00:12
So let's use the top left entry to cancel out the entries in the first column.
00:19
And so we're going to do the second row minus the first, which gives us 0, minus 1, minus 1, and positive 1.
00:32
And then we'll do the last row minus two of the first row, which gives us 0, minus 1, and 3.
00:44
All right, and now we'll continue a row reduction.
00:47
We'll rewrite our first two rows.
00:55
And then we'll replace our last row with the last row minus the second row, which is going to give us 0, 0, 0, and that's going to give us.
01:08
A 2.
01:11
All right.
01:12
And so here we see that we have 0 equals 2, which implies that we have an inconsistent solution.
01:18
So b is not in the column space of a for part a of our problem...