Wrote out chapters 2-4

chapter-1/linear-combinations-and-systems-of-linear-equations.tex

@@ -7,7 +7,7 @@
 
 \begin{definition}
 	\hfill\\
-	Let $S$ be a nonempty subset of a vector space $V$. The \textbf{span} of $S$, denoted $\text{span}(S)$, is the set consisting of all linear combinations of the vectors in $S$. For convenience, we define $\text{span}(\emptyset) = \{0\}$.
+	Let $S$ be a nonempty subset of a vector space $V$. The \textbf{span} of $S$, denoted $\lspan{S}$, is the set consisting of all linear combinations of the vectors in $S$. For convenience, we define $\lspan{\emptyset} = \{0\}$.
 \end{definition}
 
 \begin{theorem}
@@ -18,4 +18,4 @@
 \begin{definition}
 	\hfill\\
 	A subset $S$ of a vector space $V$ \textbf{generates} (or \textbf{spans}) $V$ if $\text{span}(S) = V$. In this case, we also say that the vectors of $S$ generate (or span) $V$.
-\end{definition}
+\end{definition}