\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\documentclass[10pt, a4paper]{article}
\usepackage{fullpage}
\usepackage[top=2cm, bottom=4.5cm, left=2.5cm, right=2.5cm]{geometry}
\usepackage{amsmath,amsthm,amsfonts,amssymb,amscd}
\usepackage{mathrsfs}
\usepackage{fontspec}
\usepackage[math-style=ISO]{unicode-math}
\setmathfont{TeX Gyre Termes Math}
\usepackage{lastpage}
\usepackage{enumitem}
\usepackage{enumerate}
\usepackage{fancyhdr}
\usepackage{mathrsfs}
\usepackage[dvipsnames]{xcolor}
\usepackage{graphicx}
\usepackage{listings}
\usepackage{hyperref}
\usepackage{sectsty}
\usepackage{thmtools}
\usepackage{shadethm}
\usepackage{graphicx}
\definecolor{answer_color}{HTML}{F7F8E0}
\newshadetheorem{question}{Question}
\declaretheorem[shaded={bgcolor=answer_color}]{My Answer}
\declaretheorem[shaded={bgcolor=green!80!black!30}]{True Answer}
% \begin{question} \end{questsion}
% \begin{My Answer} \end{My Answer}
% \begin{True Answer} \end{True Answer]
\hypersetup{%
colorlinks=true,
linkcolor=blue,
linkbordercolor={0 0 1}
}
\renewcommand\lstlistingname{Algorithm}
\renewcommand\lstlistlistingname{Algorithms}
\def\lstlistingautorefname{Alg.}
\lstdefinestyle{Python}{
language = Python,
frame = lines,
basicstyle = \footnotesize,
keywordstyle = \color{blue},
stringstyle = \color{green},
commentstyle = \color{red}\ttfamily
}
\setlength{\parindent}{0.0in}
\setlength{\parskip}{0.05in}
% Edit these as appropriate
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand\course{Course Name}
\newcommand\hwnumber{1} % <-- homework number
\newcommand\Informationa{John Smith/12345678}
%\newcommand\Informationb{John Smith/12345678}
\pagestyle{fancy}
\headheight 35pt
\lhead{\course \\ Name and ID: \Informationa}
%\lhead{\course \\ Name and ID: \Informationa \\ Name and ID: \Informationb}
\chead{\textbf{\Large Assignment \hwnumber}}
\rhead{\includegraphics[width=4cm]{logo.png} \\ \today}
\lfoot{}
\pagenumbering{roman}
\cfoot{\small\thepage}
\rfoot{}
\headsep 1.2em
\begin{document}
%% Question 1 %%
\begin{question}
Suppose $V$ is a vector space over $\mathbb{F}$ with a basis of order $n$. Then prove "Every basis of $V$ has order $n$"
\end{question}
\begin{My Answer}
Support $T$ is another basis. Since $S$ is independent and $T$ is spanning, $|T| \geq |S|$. The other direction is less trivial, since $T$ might be infitie, and Steinitz does not immediately apply. Instead, we argue as follows: since $T$ is
linearly independent, every finite subset of $T$ is independent. Also, $S$ is spanning. So every finite subset of T has order at most $|S|$. So $|T| \leq |S|$.
So $|T| = |S|$ \textit{(copy from \href{https://dec41.user.srcf.net/notes/IB_M/linear_algebra_thm_proof.pdf}{Part IB - Linear Algebra})}
\end{My Answer}
\end{document}