Meu Quarto PDF não está sendo renderizado!
Aqui está a saída de erro no terminal quando pressiono "Renderizar" no RStudio:
pandoc
to: pdf
output-file: LearningLaTeX.pdf
standalone: true
pdf-engine: latexmk
variables:
graphics: true
tables: true
default-image-extension: pdf
toc: true
metadata
documentclass: scrartcl
classoption:
- DIV=11
- numbers=noendperiod
papersize: letter
header-includes:
- '\KOMAoption{captions}{tableheading}'
block-headings: true
editor: visual
title: Learning LaTeX
author: Anish Goyal
date: 'January 18, 2023'
subtitle: A document containing a collection of mathematical expressions in LaTeX and a 'funny' meme about LaTeX for the Applications of Linear Algebra class at GSMST.
latexmk: security risk: running with elevated privileges
pdflatex: security risk: running with elevated privileges
Latexmk: If appropriate, the -f option can be used to get latexmk
to try to force complete processing.
Reverting Windows console CPs to (in,out) = (437,65001)
Error producing PDF.
! Missing \endgroup inserted.
<inserted text>
\endgroup
l.289 \[\begin{eqnarray}
Aqui está a fonte Quarto (.qmd):
---
title: "Learning LaTeX"
author: Anish Goyal
date: January 18, 2023
subtitle: "A document containing a collection of mathematical expressions in LaTeX and a 'funny' meme about LaTeX for the Applications of Linear Algebra class at GSMST."
format:
pdf:
pdf-engine: latexmk
latex-auto-install: true
code-overflow: wrap
toc: true
---
## Mathematical expressions
### Expression 1
$$
\begin{cases}
w + x +y +z=6 \\
w \hspace{90px} +y+z =4 \\
w \hspace{90px}+y \hspace{90px} =2 \\
\end{cases}
$$
$$
\Huge
\begin{cases}
w + x +y +z=6 \\
w \hspace{90px} +y+z =4 \\
w \hspace{90px}+y \hspace{90px} =2 \\
\end{cases}
$$
### Expression 2
$$
k\neq-1, 1 \\ {\frac{1}{k+1}},{\frac{1}{k+1}}
$$
$$\Huge
k\neq-1, 1 \\ {\frac{1}{k+1}},{\frac{1}{k+1}}
$$
### Expression 3
$$
\operatorname{tr}A:=\sum_{j=1}^{n}a_{jj}
$$
$$
\Huge
\operatorname{tr}A:=\sum_{j=1}^{n}a_{jj}
$$
### Expression 4
$$
A(\theta)={\left[
\begin{matrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{matrix}\right]}
$$
$$ \Huge
A(\theta)={\left[
\begin{matrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{matrix}\right]}
$$
### Expression 5
$$
A = \left [ \begin{matrix}
0 & a & a^2 & a^3 & a^4 \\
0 & 0 & a & a^2 & a^3 \\
0 & 0 & 0 & a & a^2 \\
0 & 0 & 0 & 0 & a \\
0 & 0 & 0 & 0 & 0
\end{matrix} \right ]
$$
$$ \Huge
A = \left [ \begin{matrix}
0 & a & a^2 & a^3 & a^4 \\
0 & 0 & a & a^2 & a^3 \\
0 & 0 & 0 & a & a^2 \\
0 & 0 & 0 & 0 & a \\
0 & 0 & 0 & 0 & 0
\end{matrix} \right ]
$$
### Expression 6
$$
\bf{3.1.6. Proposition.} \ Let \ n \in \mathbb{N} \ and \ \bf{M}_{n \times n} \ be \ the \ collection \ of \ all \ n \times n \ matrices. \ There \ is \ exactly \ one \\ function \\
\mathrm{det}: \bf{M}_{n \times n} \rightarrow \mathbb{R}\colon A\mapsto\operatorname{det}A
$$
$$\begin{eqnarray}
\bf{3.1.6. Proposition.} \ Let \ n \in \mathbb{N} \ and \ \bf{M}_{n \times n} \ be \ the \ collection \ of \ all \ n \times n \ matrices. \ There \ is \ exactly \ one \ function \\
\mathrm{det}: \bf{M}_{n \times n} \rightarrow \mathbb{R}\colon A\mapsto\operatorname{det}A
\end{eqnarray}$$
### Expression 7
$$
\bf{3.1.12. Proposition.} \ If \ A \in \mathbb{N} \ and \ 1 \le j \le n, \ then \\
\mathrm{det}\ A: \sum_{k=1}^{n}a_{jk}C_{jk}
$$
$$\Large \begin{eqnarray}
\bf{3.1.12. Proposition.} \ If \ A \in \mathbb{N} \ and \ 1 \le j \le n, \ then \\
\mathrm{det}\ A: \sum_{k=1}^{n}a_{jk}C_{jk}
\end{eqnarray}$$
### Expression 8
$$
\vert a d+b e+c f\vert\leq{\sqrt{a^{2}+b^{2}+c^{2}}}{\sqrt{d^{2}+e^{2}+f^{2}}}
$$
$$ \huge
\vert a d+b e+c f\vert\leq{\sqrt{a^{2}+b^{2}+c^{2}}}{\sqrt{d^{2}+e^{2}+f^{2}}}
$$
### Expression 9
$$
\text{Let $V$ be the set of real numbers $x$ such that $x >= 0$. Define an operation of "addition" by} \\
x \boxplus y = xy+1 \\
\text{for all $x, y \in V$. Define an operation of "scalar multiplication" by} \\
a \boxdot x = a^2x \\
\text{for all $a \in R$ and $x \in V$.}
$$
$$\begin{eqnarray}
\text{Let $V$ be the set of real numbers $x$ such that $x >= 0$. Define an operation of "addition" by} \\
x \boxplus y = xy+1 \\
\text{for all $x, y \in V$. Define an operation of "scalar multiplication" by} \\
a \boxdot x = a^2x \\
\text{for all $a \in R$ and $x \in V$.}
\end{eqnarray}$$
### Expression 10
$$
\left [ \begin{matrix}
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & 1 & 0 & 0 & 0 \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 1 & 0 & 0 \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & 0 & 0 & 1 & 0 \\
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 0 & 0 & 1 \\
\end{matrix} \right ] \xrightarrow{X_1}
\left [ \begin{matrix}
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & & & & \\
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & & & & \\
\end{matrix} \right ]
$$
$$ \Large
\left [ \begin{matrix}
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & 1 & 0 & 0 & 0 \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 1 & 0 & 0 \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & 0 & 0 & 1 & 0 \\
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 0 & 0 & 1 \\
\end{matrix} \right ] \xrightarrow{X_1}
\left [ \begin{matrix}
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & & & & \\
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & & & & \\
\end{matrix} \right ]
$$
### Expression 11
$$
a_{jk} = \begin{cases}
0, & \text{for $\vert j-k \vert 1$} \\
1, &\text{for $\vert j-k \vert = 1$} \\
2\cos x, &\text{for $j=k$} \\
\end{cases}
$$
$$ \Huge
a_{jk} = \begin{cases}
0, & \text{for $\vert j-k \vert 1$} \\
1, &\text{for $\vert j-k \vert = 1$} \\
2\cos x, &\text{for $j=k$} \\
\end{cases}
$$
### Expression 12
$$
\bf{4.1.3. Definition.} \text{ Let $\bf{x}$ and $\bf{y}$ be nonzero vectors in $\mathbb{R}^n$. Then $\measuredangle{(\bf{x}, \bf{y})}$, the ANGLE between $\bf{x}$ and $\bf{y}$, is defined by} \\
\measuredangle{(\bf{x}, \bf{y})} = \arccos \frac{\langle \bf{x}, \bf{y}\rangle}{\Vert\bf{x} \Vert \Vert\bf{y} \Vert}
$$
$$\begin{eqnarray}
\bf{4.1.3. Definition.} \text{ Let $\bf{x}$ and $\bf{y}$ be nonzero vectors in $\mathbb{R}^n$. Then $\measuredangle{(\bf{x}, \bf{y})}$, the ANGLE between $\bf{x}$ and $\bf{y}$, is defined by} \\
\measuredangle{(\bf{x}, \bf{y})} = \arccos \frac{\langle \bf{x}, \bf{y}\rangle}{\Vert\bf{x} \Vert \Vert\bf{y} \Vert}
\end{eqnarray}$$
### Expression 13
$$
M\cap N \\
M\cup N
$$
$$ \huge \begin{eqnarray}
M\cap N \\
M\cup N
\end{eqnarray} $$
### Expression 14
$$
\int_{0}^{1}t g(t)\,d t=0 \hspace{50pt} \text{and} \hspace{50pt} \int_{0}^{1}t^{4}g(t)\,d t=0
$$
$$ \huge \begin{eqnarray}
\int_{0}^{1}t g(t)\,d t=0 \hspace{50pt} \text{and} \hspace{50pt} \int_{0}^{1}t^{4}g(t)\,d t=0
\end{eqnarray}$$
### Expression 15
$$
\mathbf{y}=\left(-{\frac{1}{2}},{\frac{\sqrt{3}}{2}}\right)
$$
$$ \huge
\mathbf{y}=\left(-{\frac{1}{2}},{\frac{\sqrt{3}}{2}}\right)
$$
## A LaTeX Meme
Aqui está o arquivo LaTeX (.tex) real produzido:
% Options for packages loaded elsewhere
\PassOptionsToPackage{unicode}{hyperref}
\PassOptionsToPackage{hyphens}{url}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
%
\documentclass[
letterpaper,
DIV=11,
numbers=noendperiod]{scrartcl}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
\usepackage{iftex}
\ifPDFTeX
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{textcomp} % provide euro and other symbols
\else % if luatex or xetex
\usepackage{unicode-math}
\defaultfontfeatures{Scale=MatchLowercase}
\defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
\fi
% Use upquote if available, for straight quotes in verbatim environments
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
\IfFileExists{microtype.sty}{% use microtype if available
\usepackage[]{microtype}
\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
}{}
\makeatletter
\@ifundefined{KOMAClassName}{% if non-KOMA class
\IfFileExists{parskip.sty}{%
\usepackage{parskip}
}{% else
\setlength{\parindent}{0pt}
\setlength{\parskip}{6pt plus 2pt minus 1pt}}
}{% if KOMA class
\KOMAoptions{parskip=half}}
\makeatother
\usepackage{xcolor}
\setlength{\emergencystretch}{3em} % prevent overfull lines
\setcounter{secnumdepth}{-\maxdimen} % remove section numbering
% Make \paragraph and \subparagraph free-standing
\ifx\paragraph\undefined\else
\let\oldparagraph\paragraph
\renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}}
\fi
\ifx\subparagraph\undefined\else
\let\oldsubparagraph\subparagraph
\renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}}
\fi
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}\usepackage{longtable,booktabs,array}
\usepackage{calc} % for calculating minipage widths
% Correct order of tables after \paragraph or \subparagraph
\usepackage{etoolbox}
\makeatletter
\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{}
\makeatother
% Allow footnotes in longtable head/foot
\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}}
\makesavenoteenv{longtable}
\usepackage{graphicx}
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
\makeatother
% Scale images if necessary, so that they will not overflow the page
% margins by default, and it is still possible to overwrite the defaults
% using explicit options in \includegraphics[width, height, ...]{}
\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
% Set default figure placement to htbp
\makeatletter
\def\fps@figure{htbp}
\makeatother
\KOMAoption{captions}{tableheading}
\makeatletter
\makeatother
\makeatletter
\makeatother
\makeatletter
\@ifpackageloaded{caption}{}{\usepackage{caption}}
\AtBeginDocument{%
\ifdefined\contentsname
\renewcommand*\contentsname{Table of contents}
\else
\newcommand\contentsname{Table of contents}
\fi
\ifdefined\listfigurename
\renewcommand*\listfigurename{List of Figures}
\else
\newcommand\listfigurename{List of Figures}
\fi
\ifdefined\listtablename
\renewcommand*\listtablename{List of Tables}
\else
\newcommand\listtablename{List of Tables}
\fi
\ifdefined\figurename
\renewcommand*\figurename{Figure}
\else
\newcommand\figurename{Figure}
\fi
\ifdefined\tablename
\renewcommand*\tablename{Table}
\else
\newcommand\tablename{Table}
\fi
}
\@ifpackageloaded{float}{}{\usepackage{float}}
\floatstyle{ruled}
\@ifundefined{c@chapter}{\newfloat{codelisting}{h}{lop}}{\newfloat{codelisting}{h}{lop}[chapter]}
\floatname{codelisting}{Listing}
\newcommand*\listoflistings{\listof{codelisting}{List of Listings}}
\makeatother
\makeatletter
\@ifpackageloaded{caption}{}{\usepackage{caption}}
\@ifpackageloaded{subcaption}{}{\usepackage{subcaption}}
\makeatother
\makeatletter
\@ifpackageloaded{tcolorbox}{}{\usepackage[many]{tcolorbox}}
\makeatother
\makeatletter
\@ifundefined{shadecolor}{\definecolor{shadecolor}{rgb}{.97, .97, .97}}
\makeatother
\makeatletter
\makeatother
\ifLuaTeX
\usepackage{selnolig} % disable illegal ligatures
\fi
\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
\urlstyle{same} % disable monospaced font for URLs
\hypersetup{
pdftitle={Learning LaTeX},
pdfauthor={Anish Goyal},
colorlinks=true,
linkcolor={blue},
filecolor={Maroon},
citecolor={Blue},
urlcolor={Blue},
pdfcreator={LaTeX via pandoc}}
\title{Learning LaTeX}
\usepackage{etoolbox}
\makeatletter
\providecommand{\subtitle}[1]{% add subtitle to \maketitle
\apptocmd{\@title}{\par {\large #1 \par}}{}{}
}
\makeatother
\subtitle{A document containing a collection of mathematical expressions
in LaTeX and a `funny' meme about LaTeX for the Applications of Linear
Algebra class at GSMST.}
\author{Anish Goyal}
\date{1/18/23}
\begin{document}
\maketitle
\ifdefined\Shaded\renewenvironment{Shaded}{\begin{tcolorbox}[enhanced, interior hidden, borderline west={3pt}{0pt}{shadecolor}, breakable, frame hidden, boxrule=0pt, sharp corners]}{\end{tcolorbox}}\fi
\renewcommand*\contentsname{Table of contents}
{
\hypersetup{linkcolor=}
\setcounter{tocdepth}{3}
\tableofcontents
}
\hypertarget{mathematical-expressions}{%
\subsection{Mathematical expressions}\label{mathematical-expressions}}
\hypertarget{expression-1}{%
\subsubsection{Expression 1}\label{expression-1}}
\includegraphics{images/image-1069874928.png}
\begin{verbatim}
$$
\begin{cases}
w + x +y +z=6 \\
w \hspace{90px} +y+z =4 \\
w \hspace{90px}+y \hspace{90px} =2 \\
\end{cases}
$$
\end{verbatim}
\[
\Huge
\begin{cases}
w + x +y +z=6 \\
w \hspace{90px} +y+z =4 \\
w \hspace{90px}+y \hspace{90px} =2 \\
\end{cases}
\]
\hypertarget{expression-2}{%
\subsubsection{Expression 2}\label{expression-2}}
\includegraphics{images/image-1212342519.png}
\begin{verbatim}
$$
k\neq-1, 1 \\ {\frac{1}{k+1}},{\frac{1}{k+1}}
$$
\end{verbatim}
\[\Huge
k\neq-1, 1 \\ {\frac{1}{k+1}},{\frac{1}{k+1}}
\]
\hypertarget{expression-3}{%
\subsubsection{Expression 3}\label{expression-3}}
\includegraphics{images/image-1884990960.png}
\begin{verbatim}
$$
\operatorname{tr}A:=\sum_{j=1}^{n}a_{jj}
$$
\end{verbatim}
\[
\Huge
\operatorname{tr}A:=\sum_{j=1}^{n}a_{jj}
\]
\hypertarget{expression-4}{%
\subsubsection{Expression 4}\label{expression-4}}
\includegraphics{images/image-1983034508.png}
\begin{verbatim}
$$
A(\theta)={\left[
\begin{matrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{matrix}\right]}
$$
\end{verbatim}
\[ \Huge
A(\theta)={\left[
\begin{matrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{matrix}\right]}
\]
\hypertarget{expression-5}{%
\subsubsection{Expression 5}\label{expression-5}}
\includegraphics{images/image-1969377765.png}
\begin{verbatim}
$$
A = \left [ \begin{matrix}
0 & a & a^2 & a^3 & a^4 \\
0 & 0 & a & a^2 & a^3 \\
0 & 0 & 0 & a & a^2 \\
0 & 0 & 0 & 0 & a \\
0 & 0 & 0 & 0 & 0
\end{matrix} \right ]
$$
\end{verbatim}
\[ \Huge
A = \left [ \begin{matrix}
0 & a & a^2 & a^3 & a^4 \\
0 & 0 & a & a^2 & a^3 \\
0 & 0 & 0 & a & a^2 \\
0 & 0 & 0 & 0 & a \\
0 & 0 & 0 & 0 & 0
\end{matrix} \right ]
\]
\hypertarget{expression-6}{%
\subsubsection{Expression 6}\label{expression-6}}
\includegraphics{images/image-1950951149.png}
\begin{verbatim}
$$
\textbf{3.1.6. Proposition.} \ Let \ n \in \mathbb{N} \ and \ \textbf{M}_{n \times n} \ be \ the \ collection \ of \ all \ n \times n \ matrices. \ There \ is \ exactly \ one \\ function \\
\mathrm{det}: \textbf{M}_{n \times n} \rightarrow \mathbb{R}\colon A\mapsto\operatorname{det}A
$$
\end{verbatim}
\[
\textbf{3.1.6. Proposition.} \ Let \ n \in \mathbb{N} \ and \ \textbf{M}_{n \times n} \ be \ the \ collection \ of \ all \ n \times n \ matrices. \ There \ is \ exactly \ one \ function \\
\mathrm{det}: \textbf{M}_{n \times n} \rightarrow \mathbb{R}\colon A\mapsto\operatorname{det}A
\]
\hypertarget{expression-7}{%
\subsubsection{Expression 7}\label{expression-7}}
\includegraphics{images/image-2143312636.png}
\begin{verbatim}
$$
\textbf{3.1.12. Proposition.} \ If \ A \in \mathbb{N} \ and \ 1 \le j \le n, \ then \\
\mathrm{det}\ A: \sum_{k=1}^{n}a_{jk}C_{jk}
$$
\end{verbatim}
\[\Large \begin{eqnarray}
\textbf{3.1.12. Proposition.} \ If \ A \in \mathbb{N} \ and \ 1 \le j \le n, \ then \\
\mathrm{det}\ A: \sum_{k=1}^{n}a_{jk}C_{jk}
\end{eqnarray}\]
\hypertarget{expression-8}{%
\subsubsection{Expression 8}\label{expression-8}}
\includegraphics{images/image-1940893679.png}
\begin{verbatim}
$$
\vert a d+b e+c f\vert\leq{\sqrt{a^{2}+b^{2}+c^{2}}}{\sqrt{d^{2}+e^{2}+f^{2}}}
$$
\end{verbatim}
\[ \huge
\vert a d+b e+c f\vert\leq{\sqrt{a^{2}+b^{2}+c^{2}}}{\sqrt{d^{2}+e^{2}+f^{2}}}
\]
\hypertarget{expression-9}{%
\subsubsection{Expression 9}\label{expression-9}}
\includegraphics{images/image-331355199.png}
\begin{verbatim}
$$
\text{Let $V$ be the set of real numbers $x$ such that $x >= 0$. Define an operation of "addition" by} \\
x \boxplus y = xy+1 \\
\text{for all $x, y \in V$. Define an operation of "scalar multiplication" by} \\
a \boxdot x = a^2x \\
\text{for all $a \in R$ and $x \in V$.}
$$
\end{verbatim}
\[\begin{eqnarray}
\text{Let $V$ be the set of real numbers $x$ such that $x >= 0$. Define an operation of "addition" by} \\
x \boxplus y = xy+1 \\
\text{for all $x, y \in V$. Define an operation of "scalar multiplication" by} \\
a \boxdot x = a^2x \\
\text{for all $a \in R$ and $x \in V$.}
\end{eqnarray}\]
\hypertarget{expression-10}{%
\subsubsection{Expression 10}\label{expression-10}}
\includegraphics{images/image-1239672658.png}
\begin{verbatim}
$$
\left [ \begin{matrix}
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & 1 & 0 & 0 & 0 \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 1 & 0 & 0 \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & 0 & 0 & 1 & 0 \\
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 0 & 0 & 1 \\
\end{matrix} \right ] \xrightarrow{X_1}
\left [ \begin{matrix}
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & & & & \\
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & & & & \\
\end{matrix} \right ]
$$
\end{verbatim}
\[ \Large
\left [ \begin{matrix}
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & 1 & 0 & 0 & 0 \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 1 & 0 & 0 \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & 0 & 0 & 1 & 0 \\
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & 0 & 0 & 0 & 1 \\
\end{matrix} \right ] \xrightarrow{X_1}
\left [ \begin{matrix}
1 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
0 & 0 & \frac{1}{2} & \frac{1}{2} & : & & & & \\
\frac{1}{2} & 0 & -\frac{1}{2} & 0 & : & & & & \\
0 & -\frac{1}{2} & 0 & \frac{1}{2} & : & & & & \\
\end{matrix} \right ]
\]
\hypertarget{expression-11}{%
\subsubsection{Expression 11}\label{expression-11}}
\includegraphics{images/image-966103750.png}
\begin{verbatim}
$$
a_{jk} = \begin{cases}
0, & \text{for $\vert j-k \vert 1$} \\
1, &\text{for $\vert j-k \vert = 1$} \\
2\cos x, &\text{for $j=k$} \\
\end{cases}
$$
\end{verbatim}
\[ \Huge
a_{jk} = \begin{cases}
0, & \text{for $\vert j-k \vert 1$} \\
1, &\text{for $\vert j-k \vert = 1$} \\
2\cos x, &\text{for $j=k$} \\
\end{cases}
\]
\hypertarget{expression-12}{%
\subsubsection{Expression 12}\label{expression-12}}
\includegraphics{images/image-698644403.png}
\begin{verbatim}
$$
\textbf{4.1.3. Definition.} \text{ Let $\textbf{x}$ and $\textbf{y}$ be nonzero vectors in $\mathbb{R}^n$. Then $\measuredangle{(\textbf{x}, \textbf{y})}$, the ANGLE between $\textbf{x}$ and $\textbf{y}$, is defined by} \\
\measuredangle{(\textbf{x}, \textbf{y})} = \arccos \frac{\langle \textbf{x}, \textbf{y}\rangle}{\Vert\textbf{x} \Vert \Vert\textbf{y} \Vert}
$$
\end{verbatim}
\[\begin{eqnarray}
\textbf{4.1.3. Definition.} \text{ Let $\textbf{x}$ and $\textbf{y}$ be nonzero vectors in $\mathbb{R}^n$. Then $\measuredangle{(\textbf{x}, \textbf{y})}$, the ANGLE between $\textbf{x}$ and $\textbf{y}$, is defined by} \\
\measuredangle{(\textbf{x}, \textbf{y})} = \arccos \frac{\langle \textbf{x}, \textbf{y}\rangle}{\Vert\textbf{x} \Vert \Vert\textbf{y} \Vert}
\end{eqnarray}\]
\hypertarget{expression-13}{%
\subsubsection{Expression 13}\label{expression-13}}
\includegraphics{images/image-1340050623.png}
\begin{verbatim}
$$
M\cap N \\
M\cup N
$$
\end{verbatim}
\[ \huge \begin{eqnarray}
M\cap N \\
M\cup N
\end{eqnarray} \]
\hypertarget{expression-14}{%
\subsubsection{Expression 14}\label{expression-14}}
\includegraphics{images/image-341248740.png}
\begin{verbatim}
$$
\int_{0}^{1}t g(t)\,d t=0 \hspace{50pt} \text{and} \hspace{50pt} \int_{0}^{1}t^{4}g(t)\,d t=0
$$
\end{verbatim}
\[ \huge \begin{eqnarray}
\int_{0}^{1}t g(t)\,d t=0 \hspace{50pt} \text{and} \hspace{50pt} \int_{0}^{1}t^{4}g(t)\,d t=0
\end{eqnarray}\]
\hypertarget{expression-15}{%
\subsubsection{Expression 15}\label{expression-15}}
\includegraphics{images/image-1876561767.png}
\begin{verbatim}
$$
\mathbf{y}=\left(-{\frac{1}{2}},{\frac{\sqrt{3}}{2}}\right)
$$
\end{verbatim}
\[ \huge
\mathbf{y}=\left(-{\frac{1}{2}},{\frac{\sqrt{3}}{2}}\right)
\]
\hypertarget{a-latex-meme}{%
\subsection{A LaTeX Meme}\label{a-latex-meme}}
\includegraphics{images/image-220842989.png}
\end{document}
Tentei usar um mecanismo de PDF diferente (xelatex ou latexmk), sem sucesso! Tentei me livrar da matriz de equações e ainda não funciona. Também tentei usar o RStudio em vez do VS Code para renderizar esse arquivo e não funcionou.
Responder1
As mensagens de erro que você recebe são de aninhamento de ambientes matemáticos, como eqnarrayem outros ambientes matemáticos como $$...$$e \[...\], uso de comandos de fonte desatualizados, como \bfem uma classe koma, etc.
No entanto, em vez de corrigir esses problemas, você não deve abusar dos ambientes matemáticos para digitar frases inteiras. Em vez disso, dê uma olhada nos vários pacotes de teoremas para definir adequadamente suas partes semelhantes a teoremas (por exemplo, suas proposições). Aqui um exemplo com o amsthmpacote:
---
title: "Learning LaTeX"
author: Anish Goyal
date: January 18, 2023
subtitle: "A document containing a collection of mathematical expressions in LaTeX and a 'funny' meme about LaTeX for the Applications of Linear Algebra class at GSMST."
format:
pdf:
pdf-engine: latexmk
latex-auto-install: true
code-overflow: wrap
toc: true
header-includes:
- \usepackage{amsthm}
- \newtheorem{proposition}{Proposition}
---
\begin{proposition}
If $A \in \mathbb{N}$ and $1 \le j \le n$, then
\begin{equation}
\det A: \sum_{k=1}^{n}a_{jk}C_{jk}
\end{equation}
\end{proposition}
