• Title: Linear Subspaces

• Series: Abstract Linear Algebra

• YouTube-Title: Abstract Linear Algebra 3 | Linear Subspaces

• Bright video: https://youtu.be/Ek5Ebm6t6nY

• Dark video: https://youtu.be/d77TOcT_Eeo

• Quiz: Test your knowledge

• Subtitle on GitHub: ala03_sub_eng.srt missing

• Timestamps (n/a)
• Subtitle in English (n/a)
• Quiz Content

Q1: Let $V$ be a vector space with zero vector $\mathbf{o}$. Which claim is correct?

A1: $0 \cdot v = \mathbf{o}$ for all $v \in V$.

A2: $(-1) \cdot v = \mathbf{o}$ for all $v \in V$.

A3: $\lambda \cdot v = \mathbf{o}$ for all $v \in V$ and all $\lambda \in \mathbb{F}$.

A4: $(-1) \cdot v + v = v$ for all $v \in V$.

Q2: Let $V$ be a vector space and $U \subseteq V$ a subspace. What is not correct in general?

A1: $u + v \in U$ for each $u \in U$ and $v \in V$.

A2: $u + v \in U$ for all $u,v \in U$.

A3: $\lambda \cdot u \in U$ for all $u \in U$ and all $\lambda \in \mathbb{F}$.

A4: The zero vector lies in $U$.

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