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\begin{document}

\title[101 Homework \#7]{Math 101: Algebra I \\ Worksheet, Day \#7}
\date{Assigned Wednesday, 21 September 2016; due Friday, 23 September 2016}

\maketitle

\begin{problab}{JV7.A}
Let $F$ be a field, let $V$ be an $F$-vector space, and let $W \subseteq V$ be an $F$-subspace.  Show that $(V/W)^* \simeq \ann(W)$.
\end{problab}

\begin{problab}{JV7.B}
Let $F$ be a field and let $V,W$ be $F$-vector spaces.  [Try not to assume that $V,W$ are finite-dimensional.]  Let $\phi \in \Hom_F(V,W)$.  Show that $\img(\phi^*)=\ann(\ker \phi)$.
\end{problab}

\end{document}