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Title: Determinant (Overview)
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Series: Linear Algebra
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Chapter: Determinants
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YouTube-Title: Linear Algebra 43 | Determinant (Overview)
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Bright video: Watch on YouTube
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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: la43_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
00:00 Intro
00:50 Determinant of a matrix A
01:32 First property of determinant
03:40 Second property of determinant
04:57 Third property of determinant
06:50 Credits
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Subtitle in English (n/a)
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Quiz Content
Q1: Which property is not one of the determinant?
A1: $| \det(A) |$ is the volume of the parallelepiped spanned by the columns of $A$.
A2: $\det(A)$ is zero if and only if the columns of $A$ are linearly independent.
A3: $\det(\mathbf{1}) = 1$
A4: The sign of $\det(A)$ gives orientation of the vectors given by the columns of $A$.
Q2: Which statement is correct?
A1: $\det \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} = 1$
A2: $\det \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} = -1$
A3: $\det \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} = 0$
A4: One needs more information.
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Last update: 2024-10
