Question

In a n by m matrix, what would be the dimension of the subspace?

Answer 1

dimension of subspace 1 by m

Answer 2

If a matrix is an n x m matrix, then it is a linear transformation that takes in vectors from R^m, and spits out vectors in R^n. In other words, if T was the linear transformation:\[T: \mathbb{R}^m\longrightarrow \mathbb{R}^n\]
The question "what is the dimension of the subspace" is a little vague though. Which subspace? Column Space? Null Space, Row Space? Left Null Space?

Even if we knew which space, without the specific matrix, we can answer those questions.

Answer 3

can not* answer those questions, my bad.