69 lines
996 B
TeX
Executable File
69 lines
996 B
TeX
Executable File
% use [nosolutions] flag to hide solutions.
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% use [solutions] flag to show solutions.
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\documentclass[
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solutions,
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hidewarning,
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%singlenumbering
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]{../../resources/ormc_handout}
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%\usepackage{lua-visual-debug}
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\usepackage{tikz-3dplot}
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\usetikzlibrary{
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quotes,
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angles,
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matrix,
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decorations.pathreplacing,
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calc,
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positioning,
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fit
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}
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\input{tikzset}
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\uptitlel{Advanced 2}
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\uptitler{Spring 2023}
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\title{Linear Algebra 101}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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\input{parts/0 notation}
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\input{parts/1 vectors}
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\input{parts/2 dotprod}
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\input{parts/3 matrices}
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\section{Bonus}
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\problem{}
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Show that the euclidean norm satisfies the triangle inequalty:
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$$
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||x+y|| \leq ||x|| + ||y||
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$$
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\vfill
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\problem{}
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Show that the eucidean norm satisfies the reverse triangle inequality:
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$$
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||x-y|| \geq |~||x|| - ||y||~|
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$$
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\vfill
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\problem{}
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Prove the Cauchy-Schwartz inequality:
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$$
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||x \cdot y|| \leq ||x||~||y||
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$$
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\vfill
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\end{document} |