equation_cycle.tex

\documentclass{report}

\usepackage{tikz,lscape}
\pagestyle{empty}

\newcommand\diagram{
\tikz{
	
	\draw[->,ultra thick] (0,-2) -- +(0,7);
	\draw[->,ultra thick] (-2,0) -- +(7,0);

	\draw[->,thick] (0,0) -- +(2,5);
	\draw[->,thick,dashed] (0,0) -- ++(4/3,10/3) -- ++(8/3,-4/3);

	\draw[->,thick] (0,0) -- +(2,-1);
	\draw[->,thick,dashed] (0,0) -- ++(8/3,-4/3) -- ++(4/3,10/3);

	\draw[->,thick] (0,0) -- +(4,2);

}}

\begin{document}

\begin{landscape}
\scalebox{1.5}{
\noindent
\tikz{
	
	\node at (-2.375,0.5) {
		$
			\left(
				\begin{array}{rr|r}
					2 & 2 & 4\\
					5 & -1 & 2
				\end{array}
			\right)
		$
	};

	\node at (-2.375,-0.25) {Augmented Matrix};

	\draw[anchor = west, ultra thick, <->] (0,0.5) to[out=0, in=90] +(2,-2);

	\node[anchor=north] at (2,-1.6) {
		$
				\begin{array}{rcrcr}
					2x&+ & 2y&= & 4\\
					5x&- & y&= & 2
				\end{array}
		$
	};

	\node at (2,-3) {System of Equations};


	\draw[anchor = north, ultra thick, <->] (2,-3.5) to[out=-90, in=0] +(-2,-2);	

	\node at (-2.375,-5.5) {
		$
			\left(
				\begin{array}{r}
					2 \\
					5
				\end{array}
			\right)x+
			\left(
				\begin{array}{r}
					2\\
					-1
				\end{array}
			\right)y=
			\left(
				\begin{array}{r}
					4\\
					2
				\end{array}
			\right)
		$
	};

	\node at (-2.375,-6.25) {Vector Equation};


	\draw[anchor = east, ultra thick, <->] (-4.75,-5.5) to[out=180, in=-90] +(-2,2);	

	\node[anchor=south] at (-6.75,-2.6) {
		$
			\left(
				\begin{array}{rr}
					2 & 2 \\
					5 & -1 
				\end{array}
			\right)
			\left(
				\begin{array}{r}
					x\\
					y
				\end{array}
			\right)=
			\left(
				\begin{array}{r}
					4\\
					2
				\end{array}
			\right)
		$
	};

	\node at (-6.75,-3) {Matrix Equation};


	\draw[anchor = south, ultra thick, <->] (-6.75,-1.5) to[out=90, in=180] +(2,2);	

	\node at (-2.375,-2.8) {\scalebox{0.6}{\diagram}};



}}

\end{landscape}

\end{document}