Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ be given by the matrix $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & -1 & 1\\ 3& 0 & 3 \end{pmatrix}$
1) I have to determine wheter $f$ is injective or not
I think that it can not be injective, because the rows are linearly dependent, third row= 3*(first row + second row)
2) If $f$ is not injective determine two vector $u,v$ such that $f(u)=f(v)$. I am stuck at point (2). How can I determine those vectors?