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\title{Introduction to Linear Algebra and Syllabus Rundown}
\author{Abdon Morales \\ The University of Texas at Austin \\ M 340L \\ Kirk Blazek}
\date{\today \\ Day One}
%\date{} % Activate to display a given date or no date (if empty),
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\begin{document}
\maketitle
\begin{tcolorbox}[width=\textwidth,colback={white},title={Important Dates for the course!!!},colbacktitle=yellow,coltitle=blue]
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\textbf{Midterm Exam - June 21st, 2024 (24-hour window, time limit: 1 hour, and 15 minutes)} \\
\textbf{Final Exam - July 12th, 2024 (3 hours and 40 minutes time limit)}
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\end{tcolorbox}
\section*{Basic Terminology and notation}
$a_1 + a_2 x_2 + ... + a_n x_n = b$ (Linear equation) \\
$a_1, a_2, ..., a_n, b$ (known constants) \\
\begin{tcolorbox}[width=\textwidth,colback={white},title={System of linear equations},colbacktitle=yellow,coltitle=blue]
\begin{center}
$a_{1\;1} x_1 + a_{1\;2} x_2 + ... a_{1\;n} x_n = b_1$ \\
$a_{2\;1} x_1 + a_{2\;2} x_2 + ... a_{2\;n} x_n = b_2$ \\
\hrule
$a_{m\;1} x_1 + a_{m\;2} x_2 + ... a_{m\;n} x_n = b_m$
\end{center}
The solution to this system of equations is ($x_1, x_2, ..., x_n$) which satisfies every equation simultaneously.
\end{tcolorbox}

\subsection*{Example \#1}
This is a traditional way of solving this equation and others alike.
$2x + y = 1$ \\ $x - 3y = 4$

\end{document}
