handouts/Advanced/Linear Algebra 101/main.tex

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

%\usepackage{lua-visual-debug}

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

\begin{document}

	\maketitle
		<Advanced 2>
		<Spring 2023>
		{Linear Algebra 101}
		{
			Prepared by Mark on \today \\
		}


	\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:

	$$
		||\langle x, y \rangle|| = ||x||~||y||
	$$

	\vfill


\end{document}