\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\title{Exercise 8:Math Formula}
\begin{document}
	\maketitle
	\section{Numbered Equation}
	\label{sec:one}
	Add $a$ squared and $b$ squared
	to get $c$ squared. Or, using
	a more mathematical approach.
	\\
	You can use numbered equation as in section ~\ref{sec:one} or un-numbered equation as in section~\ref{sec:two}.
	\begin{equation}
	\label{eq:one}
	a^2 + b^2 = c^2
	\end{equation}
	
	\section{Numbered Equation}
	\label{sec:two}
	\begin{equation*}
	\label{eq:two}
	a^2 + b^2 = c^2
	\end{equation*}
	
	Formulas as listed in Equation~\ref{eq:one} and Equation~\ref{eq:two} are doing the same task.
	
		\section{Array Equation}
	\label{sec:three}
	\begin{equation*}
	\mathbf{X} = \left(
	\begin{array}{ccc}
	x_1 & x_2 & \ldots \\
	x_3 & x_4 & \ldots \\
	\vdots & \vdots & \ddots
	\end{array} \right)
	\end{equation*}
	
	
	\section{Multi-value Equation}
	\label{sec:four}
	\begin{equation*}
	|x| = \left\{
	\begin{array}{rl}
	-x & \text{if } x < 0,\\
	0 & \text{if } x = 0,\\
	x & \text{if } x > 0.
	\end{array} \right.
	\end{equation*}
	
	\section{Macro}
	\begin{equation}
	\mathbf{P}=
	\begin{bmatrix}
	p_{11} & p_{12} & \ldots
	& p_{1n} \\
	p_{21} & p_{22} & \ldots
	& p_{2n} \\
	\vdots & \vdots & \ddots
	& \vdots \\
	p_{m1} & p_{m2} & \ldots
	& p_{mn}\end{bmatrix}
	\end{equation}
	
	\section{Fractions}
	\begin{equation*}
	1 + (\frac{1}{1-x^{2}})^3 
	\end{equation*}
	
\end{document}