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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: https://youtu.be/eS1QJ5Sfz0Q
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Dark video: https://youtu.be/edqg1mnjsog
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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: 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: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1 \ v_2 \end{pmatrix} $$
A2: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1+ w_1 \ v_2 +w_2 \end{pmatrix} $$
A3: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1 w_1 \ v_2 w_2 \end{pmatrix} $$
A4: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1 \ v_1 \end{pmatrix} $$
Q2: On $\mathbb{R}^2$ we have two operations. How is the scalar multiplication defined?
A1: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} \lambda v_1 \ v_2 \end{pmatrix} $$
A2: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} v_1 \ \lambda v_2 \end{pmatrix} $$
A3: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} \lambda v_1 \ \lambda v_2 \end{pmatrix} $$
A4: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} \lambda v_1 \ \lambda v_2 v_1 \end{pmatrix} $$
Q3: What is $$5 \cdot \begin{pmatrix} 1 \ 2 \end{pmatrix} + \begin{pmatrix} 0 \ 1 \end{pmatrix} \text{?}$$
A1: $$\begin{pmatrix} 5 \ 10 \end{pmatrix}$$
A2: $$\begin{pmatrix} 6 \ 10 \end{pmatrix}$$
A3: $$\begin{pmatrix} 6 \ 11 \end{pmatrix}$$
A4: $$\begin{pmatrix} 5 \ 11 \end{pmatrix}$$
A5: $$\begin{pmatrix} 6 \ 12 \end{pmatrix}$$
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Last update: 2024-10
