00:01
Hello, welcome to problem 2 .4 .37.
00:03
You were asked for true or false questions.
00:05
And the first one is if a and a transpose have the same number of pivots.
00:12
And the answer to this is yes.
00:14
It's because a and a transverse have the same rank.
00:17
We've shown this earlier, and the rank indicates the number of linearly independent equations.
00:25
So they will have the same number of pivots.
00:27
So the answer to this is yes.
00:30
Or true.
00:34
Part b asks, do a and a transpose have the same left null space? an answer to this is no.
00:42
The left null space is a transpose x equal zero, and the left, or the null space is ax equals zero.
00:58
And these do not have to be the same matrices, and generally they aren't.
01:05
An example you can use is 1 -200.
01:12
This will make an easy example.
01:15
Let's move on to part c...