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Title: Linear Combinations and Inner Products in $ \mathbb{R}^2 $
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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 3 | Linear Combinations and Inner Products in ℝ²
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): Watch on YouTube
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Original video for YT-Members (dark): Watch on YouTube
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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: la03_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 $\mathbf{v},\mathbf{w} \in \mathbb{R}^2$. Is $\mathbf{v}+\mathbf{w}$ a linear combination of $\mathbf{v}$ and $\mathbf{w}$?
A1: Yes!
A2: No!
Q2: Let $\mathbf{v},\mathbf{w} \in \mathbb{R}^2$ be given by $\mathbf{v} = \begin{pmatrix} 1 \ 2 \end{pmatrix}$ and $\mathbf{w} = \begin{pmatrix} -2 \ 1 \end{pmatrix}$. Are the two vectors orthogonal?
A1: Yes!
A2: No!
Q3: Let $\mathbf{v} \in \mathbb{R}^2$ be given by $\mathbf{v} = \begin{pmatrix} 3 \ 4 \end{pmatrix}$. What is $| \mathbf{v} |$?
A1: 0
A2: 1
A3: 5
A4: $\sqrt{10}$
A5: $\sqrt{7}$
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Last update: 2024-10
