Basis for row and column space

[FourierX]

Homework Statement

Can anyone help me figure out basis for RS(A) and basis for CS (A) along with their dimension?
I mean dim CS(A) and dim RS(A)

where A is
[1 -2 4 1]
[0 7 -15 -4]
[0 0 0 0]

Homework Equations

The Attempt at a Solution

are all non zero rows the basis for RS (A)?

 

[Hurkyl]

are all non zero rows the basis for RS (A)?

You tell me? To be a basis, you need three things:
1. Each of the nonzero rows are elements of RS(A)
2. The nonzero rows span RS(A)
3. The nonzero rows are linearly independent.
(Right? This should be familiar...)

Are all of these conditions satisfied?

 

[FourierX]

yeah, right. so the dimension of the RS(A) is the number of elements of it, correct?

 

[Phrak]

What does "RS" mean?

 

[FourierX]

row space