quiz3.tex

\documentclass{article}

\usepackage{fullpage}

\begin{document}

\begin{center}
    {\bf Quiz 3}
\end{center}
Name:


\begin{enumerate}
    \item
        Let $V$ and $W$ be finite dimensional vector spaces with an one-to-one
        linear transformation $T:V\to W$. Prove that $\dim V \leq \dim W$.
        (Hint: If $X$ is a vector space with $\dim X=n$ then any linearly
        independent subset of $X$ must have cardinality less than $n$.)
        \vfill
    \item
        Let $V$ and $W$ be a finite dimensional vector spaces with a onto
        linear transformation $T:V\to W$. Let $S$ be any spanning set of $V$.
        Prove that $T(S)=\{T(s):s\in S\}$ is also spanning.
        \vfill
\end{enumerate}
    
\end{document}