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Title: Extension of Determinant
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Series: Abstract Linear Algebra
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Chapter: General linear maps
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YouTube-Title: Abstract Linear Algebra 33 | Extension of Determinant
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Subtitle on GitHub: ala33_sub_eng.srt missing
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Quiz Content
Q1: Let $\ell: V \rightarrow V$ be a linear map where $V = \mathcal{P}_3(\mathbb{R})$ and $\ell(p) = p^\prime$. What is the determinant $\mathrm{det}(\ell)$.
A1: $\mathrm{det}(\ell) = 0$
A2: $\mathrm{det}(\ell) = 3$
A3: $\mathrm{det}(\ell) = 1$
A4: $\mathrm{det}(\ell) = 2$
Q2: Let $\ell, k: V \rightarrow V$ be two bijective linear map. What is, in general, not correct?
A1: $\mathrm{det}(\ell + k) $ $= \mathrm{det}(\ell) + \mathrm{det}(k) $
A2: $\mathrm{det}(\ell) \mathrm{det}(\ell^{-1}) = 1 $
A3: $\mathrm{det}(\ell^{-1}) = \mathrm{det}(\ell)^{-1}$
A4: $\mathrm{det}(\ell) \mathrm{det}(k) $ $= \mathrm{det}(k \circ \ell) $
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Date of video: 2024-11-11
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Last update: 2025-10
