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Title: Lines 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 4 | Lines 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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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: la04_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: Which of the following sets does not describe a line in the plane?
A1:
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x + y = 2 \right\} $$A2:
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x = 2 \right\} $$A3:
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ y = 2 \right\} $$A4:
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x^2 + y^2 = 2 \right\} $$A5:
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x^2 = 0 \right\} $$Q2: What is not a possible normal vector $\mathbf{n}$ for the line
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x = 2 \right\} $$A1:
$$ \mathbf{n} = \binom{1}{0} $$A2:
$$ \mathbf{n} = \binom{0}{1} $$A3:
$$ \mathbf{n} = \binom{-2}{0} $$Q3: Does the line
$$\left\{ \binom{x}{y} \in \mathbb{R}^2 ~\bigg|~ x = 2 \right\} $$go through the origin?
A1: Yes!
A2: No!
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Last update: 2024-10
