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Title: Linear Span
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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 8 | Linear Span
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Bright video: https://youtu.be/c_hYj4AyR6I
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Dark video: https://youtu.be/f3o_SjEZPWU
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): https://youtu.be/h7JpJfAcFFk
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Original video for YT-Members (dark): https://youtu.be/okGwr0vpufQ
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Forum: Ask a question in Mattermost
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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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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la08_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $M \subseteq \mathbb{R}^n$. Is $\mathrm{Span}(M)$ a linear subspace?
A1: Yes!
A2: No!
A3: Only in special cases.
Q2: What is $\mathrm{Span}(\emptyset)$?
A1: ${ \mathbf{0} }$
A2: $ \mathbb{R}^n $
A3: ${ \mathbf{v} \in \mathbb{R}^n \mid \mathbf{v} \neq \mathbf{0} }$
Q3: Let $U,V \subseteq \mathbb{R}^n$ be two subspaces. Which claim is not correct?
A1: $U \subseteq \mathrm{Span}(U \cup V)$
A2: $V \subseteq\mathrm{Span}(U \cup V)$
A3: $U \cap V \subseteq\mathrm{Span}(U \cup V)$
A4: $\mathrm{Span}(U \cup V)$ is a subspace.
A5: ${0 } \cap \mathrm{Span}(U \cup V) = \emptyset$
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Last update: 2024-10
