# Finding basis

1. Oct 27, 2012

### charlies1902

Let's say you have a 3x3 matrix and it's invertible. Let's call it A
If you were to find a basis for the nullspace of A, would the basis just be the original 3 column vectors of A?

2. Oct 27, 2012

### Ray Vickson

What is the null space of an invertible matrix?

RGV

3. Oct 27, 2012

### charlies1902

It would be the column vectors of A right?

4. Oct 27, 2012

### Dick

Ok, so you don't know what "invertible" means. Could you maybe look it up?

5. Oct 27, 2012

### charlies1902

det≠0 and a pivot is in every column for RREF(A).

So for a 3x3 invertible matrix,it's basis is [1 0 0]^t [0 1 0]^t and [0 0 1]^t?

6. Oct 27, 2012

### Dick

That's an example of an invertible matrix. What vectors are in its null space?

7. Oct 27, 2012

### charlies1902

The 0 vector?

8. Oct 27, 2012

### Dick

Yes. Wouldn't that always be the only answer if A were invertible?

9. Oct 27, 2012

### charlies1902

I think I got it confused with the column space.
A basis for the column space for this case would be the original 3 column vectors if A right?

10. Oct 27, 2012

### Dick

Sure. "column space" is different from "null space".