quiz4.tex

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\begin{center}
    {\bf Quiz 4}
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Name:


\begin{enumerate}
    \item
        Let $V$ and $W$ be vector spaces.
        \begin{enumerate}
            \item 
                Define what is an isomorphism between $V$ and $W$.
                \vfill
            \item
                Define what is means for $V$ to be isomorphic to $W$.
                \vfill
        \end{enumerate}
    \item
        Let $V$ and $W$ be vector spaces. Let $T:V\to W$ and $U:W\to V$ be
        linear transformations so that $U\circ T:V\to V$ is an isomorphism.
        Prove that $T$ is one-to-one.
        \vfill
        \vfill
        \vfill
\end{enumerate}
    
\end{document}