Can someone please help me out with this question. If a nonzero matrix $A$ is transformed from $\mathbb{R}^3$ to $\mathbb{R}^2$, then the null space of $A$ must be a one dimensional (sub)space of $\mathbb{R}^3$.
So i know that null space of $A$ is $\{x \colon Ax=0\}$ and I also know the definition of not onto. I don't understand the whole concept of one-dimensional space and would this statement be always true?