\documentclass[12pt]{amsart}

\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amsxtra}
\usepackage{mathrsfs}
\usepackage{colonequals}

\setlength{\hfuzz}{4pt}

\newenvironment{problab}[1]
{\noindent\textbf{Problem #1}.}
{\vskip 6pt}

\theoremstyle{remark}
\newtheorem*{solu}{Solution}

\newenvironment{enumalph}
{\begin{enumerate}\renewcommand{\labelenumi}{\textnormal{(\alph{enumi})}}}
{\end{enumerate}}

\newenvironment{enumroman}
{\begin{enumerate}\renewcommand{\labelenumi}{\textnormal{(\roman{enumi})}}}
{\end{enumerate}}

\newcommand{\C}{\mathbb C}
\newcommand{\F}{\mathbb F}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\Z}{\mathbb Z}

\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\M}{M}
\DeclareMathOperator{\img}{img}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Ann}{Ann}

\usepackage{fullpage}

\begin{document}

\title[101 Homework \#26]{Math 101: Graduate Linear Algebra \\ Homework, Day \#26}
\date{Assigned Monday, 5 November 2017; due Wednesday, 8 November 2017}

\maketitle

\begin{problab}{26.1}
Let $A=\begin{pmatrix} -1 & 2 & 1 \\ -1 & 2 & 1 \\ -2 & 4 & 2 \end{pmatrix} \in \M_3(\Q)$.  Then multiplication by $A$ defines a $\Q$-linear endomorphism of $V=\Q^3$, so equips $V$ with the structure of a (torsion) $\Q[x]$-module.  Decompose $V$ into a direct sum of cyclic $\Q[x]$-modules with a basis for each.
\end{problab}

\end{document}