\documentclass[minion]{homework}
\newcommand{\Reals}{\mathbb{R}}

\doclabel{Math F651: Homework 3}
%\docauthor{Your name here.}
\docdate{Due: February 14, 2018}
\begin{document}
\begin{aproblems}



\hproblem R \& Y 3.7

\hproblem R \& Y 3.8

\hproblem Show that $C[0,1]$ with the $L^2$ norm is not complete.

\hproblem "Symmetric bilinear forms are determined by their diagonal."

Suppose $B$ and $C$ are symmetric bilinear
forms on a vector space $X$ and $B(x,x)=C(x,x)$ for all
$x\in X$.  Show that $B(x,y)=C(x,y)$ for all $x,y\in X$.

\hproblem Let $Z$ be the subset of $\ell^2$ of sequences
that are eventually zero.  Show that $\overline Z  = \ell^2$.

\hproblem R \& Y 3.10

\hproblem R \& Y 3.14

\hproblem R \& Y 3.15

\hproblem R \& Y 3.20 (a)

\end{aproblems}
\end{document}

