Linear maps (rank and nullity)

Homework Statement

A linear map T: ℝ$^{m}$-> R$^{n}$ has rank k. State the value of the nullity of T.

The Attempt at a Solution

I know that rank would be the number of leading columns in a reduced form and the nullity would simply be the number of non-leading columns, or total columns - rank.

As we are not given how many different vectors are in the matrix, I'm not too sure how to give a value.

CompuChip
Homework Helper
nullity would simply be [...] total columns - rank.

The rank is given.
What is the total number of columns for a map $\mathbb{R}^m \to \mathbb{R}^n$?

I'm inclined to say m, but I'm not entirely sure. So m - k? Considering that's the starting space if you will.

HallsofIvy
If it's a map from $\mathbb{R}^m$ to $\mathbb{R}^n$, that means that you should be able to multiply the matrix with a vector with m components, and this should give a vector with n components. If you think about the way matrix multiplication works, does the number of columns need to be m or n?