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Title: Leibniz Formula for Determinants
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Series: Linear Algebra
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Chapter: Determinants
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YouTube-Title: Linear Algebra 46 | Leibniz Formula for Determinants
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Bright video: https://youtu.be/iClIgDt55lM
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Dark video: https://youtu.be/2ddRZsBdzJc
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la46_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: What is the correct Leibniz formula for the determinant of the matrix $$ \begin{pmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \ \end{pmatrix} $$ with real entries?
A1: $$ \sum_{(j_1, j_2, j_3) \in S_3} \mathrm{sgn}( (j_1, j_2, j_3) ) a_{j_1,1 } a_{j_2,2 } a_{j_3 ,3 } $$
A2: $$ \sum_{(j_1, j_2, j_3) \in S_3} \mathrm{sgn}( (j_1, j_2, j_3) ) a_{j_1,3 } a_{j_2,2 } a_{j_3 ,1 } $$
A3: $$ \sum_{(j_1, j_2, j_3) \in S_3} \mathrm{sgn}( (j_1, j_2, j_3) ) a_{j_1,3 } a_{j_3 ,1 } $$
A4: $$ \sum_{(j_1, j_2, j_3) \in S_3} (-1 )^{n} a_{j_1,1 } a_{j_3 ,2 } a_{j_2 ,3 } $$
Q2: What is the signum of the permutation $(1,2,3,4) \leadsto (1,4,3,2)$?
A1: $-1$
A2: $+1$
A3: $0$
A4: One needs more information.
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Last update: 2024-10
