Finding the Nullspace of an Invertible 3x3 Matrix

[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?

 

[Ray Vickson]

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?

What is the null space of an invertible matrix?

RGV

 

[charlies1902]

It would be the column vectors of A right?

 

[Dick]

It would be the column vectors of A right?

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

 

[charlies1902]

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

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?

 

[Dick]

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?

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

 

[charlies1902]

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

The 0 vector?

 

[Dick]

The 0 vector?

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

 

[charlies1902]

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

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?

 

[Dick]

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?

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