00:01
So we're given this 6x3 matrix and we're told the rank of it is 3.
00:05
So we want to figure out the dimension of the null of a first.
00:09
There's actually a nice little rule for this that says, so if we're given some n by n matrix, then rank a plus dimension of the null.
00:26
So dimension of the null of a is equal to n.
00:30
So in this case, n is 3.
00:33
We know our rank is 3.
00:36
So then that tells us our dimension of our null space is just going to be 0.
00:41
So this says dimension of null space of a is equal to 0.
00:49
So this over here is going to be 0.
00:52
Now to get the dimension of the row space, this is going to be the same thing as our rank.
00:59
Because if we actually think about it, i don't remember things.
01:02
Actually say this in the book or not but i'll kind of draw it out and we'll also kind of come to the same conclusion but yeah this should also be three but let's draw what the six by three matrix might look like so six by three is rows by columns so we have six rows here with three columns here and each place where this red and glee lie intersect each other will be a position and so if we have rank 3, that means we have three pivot positions like this...