Documents/Lineáris Algebra és Geometria Vizsga/Document.tex

213 lines
5.0 KiB
TeX

% Compile twice!
% With the current MiKTeX, you need to install the beamer, and the translator packages directly form the package manager!
% !TEX root = ./Headers/PrezA4Page.tex
% Uncomment these to get the presentation form
%\documentclass{beamer}
%\geometry{paperwidth=200mm,paperheight=200mm, top=0in, bottom=0.2in, left=0.2in, right=0.2in}
% Uncomment these, and comment the 2 lines above, to get a paper-type article
%\documentclass[10pt]{article}
%\usepackage{geometry}
%\geometry{top=0.2in, bottom=0.2in, left=0.2in, right=0.2in}
%\usepackage{beamerarticle}
%\renewcommand{\\}{\par\noindent}
%\setbeamertemplate{note page}[plain]
% Half A4 geometry
%\geometry{paperwidth=105mm,paperheight=297mm,top=0.2in, bottom=0.2in, left=0.2in, right=0.2in}
% "1/3" A4 geometry
%\geometry{paperwidth=105mm,paperheight=455mm,top=0.1in, bottom=0.1in, left=0.1in, right=0.1in}
% "1/6" A4 geometry
%\geometry{paperwidth=105mm,paperheight=891mm,top=0.1in, bottom=0.1in, left=0.1in, right=0.1in}
% "1/5" A4 geometry
%\geometry{paperwidth=105mm,paperheight=740mm,top=0.1in, bottom=0.1in, left=0.1in, right=0.1in}
% "1/4" A4 geometry
%\geometry{paperwidth=105mm,paperheight=594mm,top=0.1in, bottom=0.1in, left=0.1in, right=0.1in}
% Uncomment these, to put more than one slide / page into a generated page.
%\usepackage{pgfpages}
% Choose one
%\pgfpagesuselayout{2 on 1}[a4paper]
%\pgfpagesuselayout{4 on 1}[a4paper]
%\pgfpagesuselayout{8 on 1}[a4paper]
% Includes
\usepackage{tikz}
\usepackage{tkz-graph}
\usetikzlibrary{shapes,arrows,automata}
\usepackage[T1]{fontenc}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage[utf8]{inputenc}
\usepackage{booktabs}
\usepackage{array}
\usepackage{arydshln}
\usepackage{enumerate}
\usepackage[many, poster]{tcolorbox}
\usepackage{pgf}
\usepackage[makeroom]{cancel}
\usepackage{verbatim}
\providecommand{\includecolors}{\input{../Colors/Default.tex}}% fallback definition
\includecolors
\setbeamertemplate{itemize item}{\color{black}$-$}
\setbeamertemplate{itemize subitem}{\color{black}$-$}
\setbeamercolor*{enumerate item}{fg=black}
\setbeamercolor*{enumerate subitem}{fg=black}
\setbeamercolor*{enumerate subsubitem}{fg=black}
\renewcommand{\familydefault}{\sfdefault}
%\renewcommand{\familydefault}{\rmdefault}
\renewcommand{\footnotesize}{\fontsize{1.2em}{0.2em}}
\renewcommand{\normalsize}{\fontsize{1.2em}{0.2em}}
\renewcommand{\large}{\footnotesize}
\renewcommand{\Large}{\footnotesize}
\renewcommand{\scriptsize}{\footnotesize}
\renewcommand{\LARGE}{\footnotesize}
\renewcommand{\Huge}{\footnotesize}
\renewcommand{\tiny}{\footnotesize}
\renewcommand{\small}{\footnotesize}
\fontsize{1.2em}{0.2em}
\selectfont
\newcommand{\RHuge}{\fontsize{1.8em}{0.3em}\selectfont}
\newsavebox\CBox
%\newcommand<>*\textBF[1]{\sbox\CBox{#1}\resizebox{\wd\CBox}{\ht\CBox}{\textbf#2{#1}}}
\newcommand<>*\textBF[1]{\only#2{\sbox\CBox{#1}\resizebox{\wd\CBox}{\ht\CBox}{\textbf{#1}}}}
% Beamer theme
\usetheme{boxes}
% tikz settings for the flowchart(s)
\tikzstyle{decision} = [diamond, minimum width=3cm, minimum height=1cm, text centered, draw=black, fill=green!15]
\tikzstyle{tcolorbox} = [rectangle, draw, fill=blue!15, text width=20em, text centered, minimum height=1em]
\tikzstyle{line} = [draw, -latex']
\tikzstyle{cloud} = [draw, ellipse,fill=red!20, node distance=3cm,
minimum height=2em]
\tikzstyle{arrow} = [thick,->,>=stealth]
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}
\renewcommand{\arraystretch}{1.2}
\setlength\dashlinedash{0.2pt}
\setlength\dashlinegap{1.5pt}
\setlength\arrayrulewidth{0.3pt}
\newcommand{\mtinyskip}{\vspace{0.2em}}
\newcommand{\msmallskip}{\vspace{0.3em}}
\newcommand{\mmedskip}{\vspace{0.5em}}
\newcommand{\mbigskip}{\vspace{1em}}
\renewcommand{\u}[1]{\underline{#1}}
\begin{document}
\begin{frame}[plain]
\begin{tcolorbox}[center, colback={myyellow}, coltext={black}, colframe={myyellow}]
{\RHuge Lineáris Algebra és Geometria}\\
\end{tcolorbox}
\end{frame}
%\begin{tcolorbox}[title={Def.: }]
%\end{tcolorbox}
% -------------------- Vektorok koordinátavektora --------------------
\begin{frame}[plain]
\begin{tcolorbox}[center, colback={myyellow}, coltext={black}, colframe={myyellow}]
{\RHuge Vektorok koordinátavektora}
\mmedskip
\end{tcolorbox}
\end{frame}
\begin{frame}
\begin{tcolorbox}[title={Def.: Bázis}]
A $\{b_1,b_2,b_3\}$ vektorhalmaz bázis a $V \leq \mathbb{R}^n$ altérben. Határozzuk meg a $v = 2b_1 + 3b_2 - b_3$ vektor koordinátavektorát a $\{b_1, b_2, b_3\}$ bázisban. $[v]b1,b2,b3 =$
\end{tcolorbox}
\end{frame}
%Kiegészítések / Számolások
\begin{comment}
\begin{frame}
\begin{tcolorbox}[title={Bázistranzformáció}]
Kérdés: Hány dimenziós?\\
\begin{center}
\begin{tabular}{ c|c c c c }
\hline
& a & b & c & d \\
${e_1}$ & 3 & 9 & 1 & 5 \\
${e_2}$ & 2 & 10 & 2 & 2 \\
${e_3}$ & -1 & 1 & 1 & -3 \\
${e_4}$ & 0 & -3 & -1 & 1 \\
${e_5}$ & 1 & 2 & 0 & 2 \\
\hline
\end{tabular}
\end{center}
\mmedskip
asd
\end{tcolorbox}
\end{frame}
\end{comment}
\end{document}