Suppose that $A: \mathbb{R}^k \rightarrow \mathbb{R}^n$ is a linear map and $V$ is a vector subspace of $\mathbb{R}^n$. Check that $A$ is transversal to $V$ means just $A(\mathbb{R}^k) + V = \mathbb{R}^n$.
Could anyone give me a hint on how to prove it?