% use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions.
\documentclass[
	solutions,
	hidewarning,
	%singlenumbering
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}


%\usepackage{lua-visual-debug}

\usepackage{tikz-3dplot}
\usetikzlibrary{
	quotes,
	angles,
	matrix,
	decorations.pathreplacing,
	calc,
	positioning,
	fit
}
\input{tikzset}


\uptitlel{Advanced 2}
\uptitler{Spring 2023}
\title{Linear Algebra 101}
\subtitle{Prepared by \githref{Mark} on \today}

\begin{document}

	\maketitle

	\input{parts/0 notation}
	\input{parts/1 vectors}
	\input{parts/2 dotprod}
	\input{parts/3 matrices}



	\section{Bonus}

	\problem{}
	Show that the euclidean norm satisfies the triangle inequalty:
	$$
		||x+y|| \leq ||x|| + ||y||
	$$

	\vfill

	\problem{}
	Show that the eucidean norm satisfies the reverse triangle inequality:

	$$
		||x-y|| \geq |~||x|| - ||y||~|
	$$

	\vfill

	\problem{}
	Prove the Cauchy-Schwartz inequality:

	$$
		||x \cdot y|| \leq ||x||~||y||
	$$

	\vfill


\end{document}