---
title: "TMA4300 Project 1"
author: "Author 1, Author 2"
output: pdf_document
header-includes:
  - \geometry{top=1in}
  - \usepackage{titling}
  - \pretitle{\begin{flushleft}\Huge\bfseries}
  - \posttitle{\end{flushleft}}  
  - \preauthor{\begin{flushleft}\Large}
  - \postauthor{\end{flushleft}}  
  - \predate{\begin{flushleft}\large}
  - \postdate{\end{flushleft}}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

# Problem 1

**a)** This is an equation
$$
    \mathbf{P} = \begin{bmatrix} 0 & 0 & 1 \\
                                 1 & 0 & 0 \\
                                 0 & 1 & 0 \\
                 \end{bmatrix}
$$
a numbered equation
\begin{equation}
    \pi_0 = 0.1 \label{eq:pi0},
\end{equation}
where Equation \eqref{eq:pi0} shows that...
		
**b)** \begin{figure}[ht]
 \begin{center}
%\includegraphics[width=12cm]{res1b_1.png}
 \end{center}
 \caption{Plot of realizations.} \label{fig1}
 \end{figure}
Figure \ref{fig1} shows 10 realizations.

# Problem 2

**a)** This is the answer to 2a).

This this another paragraph


		


