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Title: Vectors 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 2 | Vectors 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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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: la02_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: On $\mathbb{R}^2$ we have two operations. How is the addition defined?
A1: $ \displaystyle \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \\ w_2 \end{pmatrix} = $ $ \displaystyle \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} $
A2: $ \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \\ w_2 \end{pmatrix} = $ $ \displaystyle \begin{pmatrix} v_1+ w_1 \\ v_2 +w_2 \end{pmatrix} $
A3: $ \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \\ w_2 \end{pmatrix} = $ $ \displaystyle \begin{pmatrix} v_1 w_1 \\ v_2 w_2 \end{pmatrix} $
A4: $ \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \\ w_2 \end{pmatrix} = $ $ \displaystyle \begin{pmatrix} v_1 \\ v_1 \end{pmatrix} $
Q2: On $\mathbb{R}^2$ we have two operations. How is the scalar multiplication defined?
A1: $ \displaystyle \lambda \cdot \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} = $ $ \displaystyle \begin{pmatrix} \lambda v_1 \\ v_2 \end{pmatrix} $
A2: $ \displaystyle \lambda \cdot \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} = $ $ \displaystyle \begin{pmatrix} v_1 \\ \lambda v_2 \end{pmatrix} $
A3: $ \displaystyle \lambda \cdot \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} = $ $ \displaystyle\begin{pmatrix} \lambda v_1 \\ \lambda v_2 \end{pmatrix} $
A4: $ \displaystyle \lambda \cdot \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} = $ $ \displaystyle\begin{pmatrix} \lambda v_1 \\ \lambda v_2 v_1 \end{pmatrix} $
Q3: What is
$$5 \cdot \begin{pmatrix} 1 \\ 2 \end{pmatrix} + \begin{pmatrix} 0 \\ 1 \end{pmatrix} \text{?}$$A1: $ \displaystyle\begin{pmatrix} 5 \\ 10 \end{pmatrix}$
A2: $ \displaystyle \begin{pmatrix} 6 \\ 10 \end{pmatrix}$
A3: $ \displaystyle \begin{pmatrix} 6 \\ 11 \end{pmatrix}$
A4: $ \displaystyle \begin{pmatrix} 5 \\ 11 \end{pmatrix}$
A5: $ \displaystyle \begin{pmatrix} 6 \\ 12 \end{pmatrix}$
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Last update: 2024-10
