LaTeX class file for math homework

mathhw.cls

%=====================================================================
% File: mathhw.cls
% Author: Courtney Strachan
% Forked from Justin Wilson's Homework Class (https://gist.github.com/jhwilson/1278588)
%=====================================================================

%=====================================================================
% Packaging
%=====================================================================
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{mathhw}[2017/04/08 Math Homework Class]

\LoadClass[letterpaper, 12pt]{article}

\RequirePackage[top=1in,bottom=1in,left=1in,right=1in]{geometry}
\RequirePackage{fancyhdr} % Extensive control of page headers and footers in LaTeX2e
\RequirePackage{ifthen} % Conditional commands in LaTeX documents
%\RequirePackage{empheq} % ...
\RequirePackage{amsmath,amsthm,amssymb} % Math packages (theorem for qed, and symbols for ..)
\RequirePackage{environ} % For Linear systems array
\RequirePackage{array} % For custom matrix type that factors in negative number spacing

%=====================================================================
% Commands
%=====================================================================
% Document Initialization
\setlength{\headheight}{15pt}
\lhead{\@author}\chead{\@title}\rhead{\@date}
\lfoot{}\cfoot{Page \thepage}\rfoot{}
\pagestyle{fancy}

\fancypagestyle{firstpagestyle}
{
  \fancyhf{} % clear all header and footer fields
  \lhead{\@author \vspace*{2px}}\chead{\textbf{\Large \@title} \vspace*{1px}}\rhead{\@date \vspace*{2px}}
  \lfoot{}\cfoot{Page \thepage}\rfoot{}
}
\thispagestyle{firstpagestyle}

% PDF Setup
\ifx\pdfoutput\undefined % LaTeX
  \RequirePackage[ps2pdf,bookmarks=true]{hyperref}
  \hypersetup{
    pdfauthor   = {\@author},
    pdftitle    = {\@title},
    pdfcreator  = {LaTeX with hyperref package},
    pdfproducer = {dvips + ps2pdf}
  }
\else % PDFLaTeX
  \RequirePackage[pdftex,bookmarks=true]{hyperref}
  \hypersetup{
    pdfauthor   = {\@author},
    pdftitle    = {\@title},
    pdfcreator  = {LaTeX with hyperref package},
    pdfproducer = {dvips + ps2pdf}
  }
\pdfadjustspacing=1
\fi

% Set up counters for problems and subsections
\newcounter{ProblemNum}
\newcounter{SubProblemNum}[ProblemNum]
\newcounter{SubSubProblemNum}[SubProblemNum]

\renewcommand{\theProblemNum}{\arabic{ProblemNum}}
\renewcommand{\theSubProblemNum}{\alph{SubProblemNum}}
\renewcommand{\theSubSubProblemNum}{\roman{SubSubProblemNum}}

\newcommand*{\anyproblem}[1]{\newpage\subsection*{#1}}
\newcommand*{\problem}[1]{\stepcounter{ProblemNum}
   \anyproblem{Problem \theProblemNum. \; #1}}

\newcommand*{\anyproblemnb}[1]{\subsection*{#1}}
\newcommand*{\problemnb}[1]{\stepcounter{ProblemNum}
   \anyproblemnb{Problem \theProblemNum. \; #1}}

\newcommand*{\soln}[1]{\subsubsection*{#1}}
\newcommand*{\solution}{\soln{Solution}}

\renewcommand*{\part}{\stepcounter{SubProblemNum}
  \soln{Part (\theSubProblemNum)}}

\newcommand*{\subpart}{\stepcounter{SubSubProblemNum}
  \soln{Subpart \theSubSubProblemNum. }}

\renewcommand{\theenumi}{(\alph{enumi})}
\renewcommand{\labelenumi}{\theenumi}
\renewcommand{\theenumii}{\roman{enumii}}

% Change qed symbol
\renewcommand{\qedsymbol}{\rule{0.7em}{0.7em}}

% Column 'C': Negative number spacing fix in matrices
% i.e., aligns numbers, and adds padding for negative
% http://tex.stackexchange.com/a/178743/106637
\makeatletter
\def\zz\ignorespaces{\@ifnextchar-{}{\phantom{-}}}
\newcolumntype{C}{>{\zz}{c}}
\makeatother

% Allow for \begin{bmatrix}[rrrr]
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{#1}}
\makeatother

% Linear systems array
\makeatletter
\newcommand{\LinearSystems@SetupLets}{
  \let\col=&
  \let\+=+
  \let\-=-
  \let\===
}
\newcommand{\LinearSystems@SetupCatcodes}{
  \catcode`\&=\active
  \catcode`\+=\active
  \catcode`\-=\active
  \catcode`\==\active
  \catcode`\/=\active
}
\newcommand{\LinearSystems@Setup}{}
\begingroup
  \LinearSystems@SetupCatcodes
  \gdef\LinearSystems@Setup{
    \LinearSystems@SetupLets
    \LinearSystems@SetupCatcodes
    \newcommand&[1][0pt]{\col\hspace{##1}\col}
    \def+{\col\+{}{}\col}
    \def-{\col\-{}{}\col}
    \def={\col\={}{}\col}
    \def/{\col\/{}{}\col}
  }
\endgroup
\NewEnviron{LinearSystems}[1]{\left\{\begin{alignedat}{#1}\BODY\end{alignedat}\right.}
\let\LinearSystems@OriginalBegin\LinearSystems
\def\LinearSystems{\LinearSystems@Setup\LinearSystems@OriginalBegin}
\makeatother

\newcommand{\Span}{\mathrm{Span}}