Added subsections when they appear, added all of the appendices, and finished the packet

chapter-3/systems-of-linear-equations-computational-aspects.tex

@@ -66,6 +66,9 @@
 	\end{enumerate}
 \end{theorem}
 
+\subsection*{An Interpretation of the Reduced Row Echelon Form}
+\addcontentsline{toc}{subsection}{An Interpretation of the Reduced Row Echelon Form}
+
 \begin{theorem}
 	\hfill\\
 	Let $A$ be an $m \times n$ matrix of rank $r$, where $r > 0$, and let $B$ be the reduced row echelon form of $A$. Then

chapter-3/systems-of-linear-equations-theoretical-aspects.tex

@@ -94,6 +94,9 @@
 	Let $Ax = b$ be a system of linear equations. Then the system is consistent if and only if $\rank{A} = \rank{A|b}$.
 \end{theorem}
 
+\subsection*{An Application}
+\addcontentsline{toc}{subsection}{An Application}
+
 \begin{definition}
 	Consider a system of linear equations
 

chapter-3/the-rank-of-a-matrix-and-matrix-inverses.tex

@@ -82,6 +82,9 @@
 	\end{enumerate}
 \end{theorem}
 
+\subsection*{The Inverse of a Matrix}
+\addcontentsline{toc}{subsection}{The Inverse of a Matrix}
+
 \begin{definition}
 	\hfill\\
 	Let $A$ and $B$ be $m \times n$ and $m \times p$ matrices, respectively. By the \textbf{augmented matrix} $(A|B)$, we mean the $m \times (n \times p)$ matrix $(A\ B)$, that is, the matrix whose first $n$ columns are the columns of $A$, and whose last $p$ columns are the columns of $B$.