Exercise3.1
Prove that \(A \in \Cmm\) has full rank if and only if it maps no two distinct vectors to the same vector. That is, show that if \(x\) and \(y\) are vectors, with \(x \neq y\text{,}\) then
\begin{equation*} Ax \neq Ay \iff \Rank(A)=m. \end{equation*}