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Title: Determinant in 2 Dimensions
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Series: Linear Algebra
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Chapter: Determinants
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YouTube-Title: Linear Algebra 44 | Determinant in 2 Dimensions
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: la44_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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Related videos:
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What is the area of the parallelogram spanned by the vectors $ \begin{pmatrix} 2 \ 1 \end{pmatrix}$ and $ \begin{pmatrix} -1 \ 1 \end{pmatrix}$?
A1: 3
A2: 2
A3: -3
A4: 4
A5: -4
Q2: What is the orientated area of the square spanned by $ \begin{pmatrix} 0 \ 2 \end{pmatrix}$ and $ \begin{pmatrix} 2 \ 0 \end{pmatrix}$?
A1: -4
A2: -2
A3: 2
A4: 4
A5: 0
Q3: Assume $\mathrm{vol}_2(\mathbf{u}, \mathbf{v}) = 0$. Are the vectors $\mathbf{u}, \mathbf{v}$ linearly dependent?
A1: Yes, always.
A2: No, never. They are linearly independent.
A3: No, they are counterexamples.
A4: Yes, but only if one assumes that both vectors are non-zero.
A5: One needs more information.
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Last update: 2024-10
