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Title: Identity and Inverses
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Series: Linear Algebra
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Chapter: Matrices and linear systems
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YouTube-Title: Linear Algebra 29 | Identity and Inverses
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Bright video: https://youtu.be/JUimgJ9E4-c
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Dark video: https://youtu.be/YvlnqA2gXQk
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Ad-free video: Watch Vimeo video
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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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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: la29_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 identity matrix in $\mathbb{R}^{2 \times 3}$?
A1: It does not exist.
A2: $ \pmb1 = \begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \end{pmatrix}$
A3: $ \pmb1 = \begin{pmatrix} 1 & 0 \ 0 & 1 \ 0 & 0\end{pmatrix}$
A4: $ \pmb1 = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$
A5: $ \pmb1 = \begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{pmatrix}$
Q2: Let $\pmb1$ be the identity matrix in $\mathbb{R}^{n \times n}$. What is the map $f_{\pmb1}$?
A1: The linear map $x \mapsto x$ for all $x \in \mathbb{R}^n$.
A2: The linear map $x \mapsto 3 x$ for all $x \in \mathbb{R}^n$.
A3: The map $x \mapsto \langle x, x \rangle x$ for all $x \in \mathbb{R}^n$.
Q3: Is the matrix $ \begin{pmatrix} 1 & 1 \ 1 & 0 \end{pmatrix}$ singular?
A1: No, because $ \begin{pmatrix} 0 & 1 \ 1 & -1 \end{pmatrix}$ is the inverse of the matrix.
A2: Yes, there is no inverse matrix.
A3: No, because $ \begin{pmatrix} 1 & 1 \ 1 & 0 \end{pmatrix}$ is the inverse of the matrix.
A4: Yes, all matrices in $\mathbb{R}^{2 \times 2}$ are singular.
A5: One needs more information.
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Last update: 2024-10
