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\title{
Exam for ``Linear Algebra 4'' (6LAG4) \\ summer semester 2025/2026
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\section*{Questions set no. 1}

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\textbf{1.}
Define an affine map. Give examples of affine maps. Give examples of maps
between affine spaces which are not affine.

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\textbf{2.}
Give an example of a linear programming problem which has:
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1) exactly one solution;
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2) exactly two solutions;
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3) an infinite number of solutions.

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\textbf{3.}
Let $P_1$ and $P_2$ be projective lines in a projective space, $V_1$ and $V_2$
are vector spaces such that $P_1 = P(V_1)$ and $P_2 = P(V_2)$, and the 
vector space $V_1 + V_2$ is $4$-dimensional. Prove that $P_1$ and $P_2$ do
not intersect.


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