Linear Algebra: 4 Fundamental Subspaces

[ChEJosh]

Homework Statement

Without computing A, find the bases for the 4 fundamental subspaces.

[1 0 0][1 2 3 4]
[6 1 0][0 1 2 3]=A=LU
[9 8 1][0 0 1 2]

Homework Equations

N/A

The Attempt at a Solution

There was an "example" in the book. It just showed the answers.
It was:

[1 0 0][1 3 0 5]
[2 1 0][0 0 1 6]=A
[5 0 1][0 0 0 0]
Where
Row Space: Basis (1,3,0,5) and (0,0,1,6)
Column Space: Basis (1,2,5) and (0,1,0)

In the problem we have to do, I take it that the row space's basis is just the 3 rows of U similar the the example. But, I'm unsure of the column space. Is it the 3 columns of L?

And, also for the nullspace, I put U in its row reduced echelon form, and solved for the nullspace as one would normally do. Is this correct?

[1 2 3 4]
[0 1 2 3] -->
[0 0 1 2]

[1 0 0 0]
[0 1 0 -1]
[0 0 1 2]
So, the nullspace basis is (0,1, -2, 1)

And, since there isn't a zero row, there also isn't a left nullspace, correct?

Sorry if that's confusing. And, thank you in advance!

 

[ChEJosh]

Bump?