Solved ex 1, 2 and 4 from algebra homework 2 and added skeleton for ex 3

1 files changed, 71 insertions, 0 deletions

diff --git a/Year 1/Algebra/Homework2/Exercise3.tex b/Year 1/Algebra/Homework2/Exercise3.tex
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+++ b/Year 1/Algebra/Homework2/Exercise3.tex
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+% Document MUST be built with XeLaTeX!
+\documentclass[11pt,a4paper]{article}
+
+\usepackage[margin=1.5cm]{geometry}
+
+% Поддръжка на български език
+% Thanks to https://tex.stackexchange.com/a/136926
+\usepackage{fontspec}
+\defaultfontfeatures{Ligatures=TeX}
+\setmainfont{CMU Serif}
+\setsansfont{CMU Sans Serif}
+
+\usepackage[bulgarian,english]{babel}
+
+\usepackage{amsmath}            % Математически символи
+\usepackage{amsfonts}           % Още математически символи
+\usepackage{cancel}             % Зачертаване
+\usepackage[dvipsnames]{xcolor} % Цветни кутийки + допълнителни цветове
+\newcommand{\answerbox}[1]{\colorbox{yellow}{$\displaystyle #1$}}
+
+\usepackage{enumitem}
+\setlist[enumerate]{label=\arabic*.}
+
+\newcommand{\ex}{3 Въпрос}
+
+\usepackage[pdfauthor={Камен Димитров Младенов, КН Зимен семестър, 2021},
+		    pdftitle={Домашна работа 2 по Алгебра 1. \ex .},
+		    pdfsubject={},
+		    pdfkeywords={},
+		    colorlinks=true,
+		    urlcolor=blue]{hyperref}
+
+\title{\vspace{-1.5cm}Домашна работа 2 по Алгебра 1. \ex .}
+\author{Камен Димитров Младенов, Група 6}
+\date{14 Ноември 2021}
+
+\begin{document}
+
+\maketitle
+
+\paragraph{\colorbox{yellow}{\ex}}
+
+Да се реши матричното уравнение
+\begin{align*}
+	\left( \begin{array}{rrrr}
+		2 & 1 & 0 & -1 \\
+		3 & 2 & 1 & -1 \\
+		1 & 1 & 1 & -1 \\
+		4 & 3 & 3 & 1
+	\end{array} \right)
+	X
+	\left( \begin{array}{rrr}
+		-2 & 1 & -1 \\
+		1 & 2 & -1 \\
+		1 & -1 & 1
+	\end{array} \right)
+	=
+	\left( \begin{array}{rrr}
+		-1 & 8 & -5 \\
+		-1 & 12 & -7 \\
+		2 & 6 & -3 \\
+		-3 & 13 & -7
+	\end{array} \right)
+\end{align*}
+с числови коефициенти.
+
+\paragraph{Решение:}
+
+[TODO]
+
+\end{document}
\ No newline at end of file