Basis for null space, row space, dimension

[Maxwhale]

Homework Statement

What are

the basis for the row space and null space for the following matrix? Find the dimension of RS, dim of NS.

[1 -2 4 1]
[3 1 -3 -1]
[5 -3 5 1]

Homework Equations

dim RS + dim NS = # of columns

The Attempt at a Solution

I reduced the matrix into row echelon form and tried to determine everything, but in vain.

 

[PowerIso]

Come on, this is a pretty fundamental question. If you want to find the row space, you are going to want to row reduce the matrix and use all the nonzero rows as a basis.

To find the null space, set Ax = 0 and solve [ A 0] and right the solution in parametric form. Take the vectors you have in parametric form as your basis.