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Title: Linear Subspaces
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Series: Linear Algebra
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Chapter: Vectors in $ \mathbb{R}^n $
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YouTube-Title: Linear Algebra 6 | Linear Subspaces
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Bright video: https://youtu.be/TITspOSjMZw
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Dark video: https://youtu.be/-haS6TdpcSU
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la06_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $U \subseteq \mathbb{R}^n$ be a subspace. Which statement is not correct?
A1: $\mathbf{0} \in U$.
A2: For $\mathbf{u}, \mathbf{v} \in U$, we have $\mathbf{u} - 2 \mathbf{v} \in U$.
A3: For $\mathbf{u}, \mathbf{v} \in U$, we have $5 \mathbf{u} - 8 \mathbf{v} \in U$.
A4: For $\mathbf{u} \in U$, we have $3\mathbf{u} \notin U$.
Q2: Which of the following subsets in $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^2$?
A1: ${ \mathbf{v} \in \mathbb{R}^2 \mid \mathbf{v} \neq \mathbf{0} }$
A2: ${ \mathbf{0} }$
A3: ${ \mathbf{v} \in \mathbb{R}^2 \mid \mathbf{v} = \mathbf{0} }$
A4: $ \mathbb{R}^2 $
A5: $\left{ \binom{v_1}{v_2} \in \mathbb{R}^2 \mid v_1 + v_2 = 0 \right}$
Q3: Let $U,V \subseteq \mathbb{R}^n$ be two subspaces. Is the intersection $U \cap V$ a subspace as well?
A1: Yes!
A2: No!
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Last update: 2024-10