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\begin{document}

\title{
Exam for ``Linear Algebra 4'' (6LAG4) \\ 
summer semester 2023/2024
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\section*{Questions set no. 3}

\vskip 20pt

\textbf{1.}
Give the definition of the affine extension of a group. Illustrate this notion
by examples. Does every group have an affine extension?


\vskip 20pt 


\textbf{2.}
Does there exist:
\\
1) an affine space
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2) an affine Euclidean space
\\
\((A,V)\) such that its ``affine part'' $A$ contains exactly:
\\
a) $5$ points?
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b) $2024$ points?


\vskip 20pt 


\textbf{3.}
In the Euclidean affine space $\mathbb R^3$, find the distance between the point
$(0,0,0)$ and the affine subspace 
$\set{(2\lambda + \mu, 3 + 2\lambda + 2\mu, 4 + 3\lambda + 2\mu)}{\lambda, \mu \in \mathbb R}$.




\end{document}
