Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{Z}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by Exercise LT.M60, $Z$ is a linear transformation. Formulate a condition on $U$ that is equivalent to $Z$ being an injective linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is injective if and only if $U$ is $\Rule{1in}{1pt}{0pt}$. (See Exercise SLT.M60, Exercise IVLT.M60.)