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Title: Similar Matrices
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Series: Abstract Linear Algebra
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YouTube-Title: Abstract Linear Algebra 30 | Similar Matrices
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Bright video: https://youtu.be/eOOAHKikbcI
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Dark video: https://youtu.be/ktdlPgXccns
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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: ala30_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Which of the following matrices is similar to the zero matrix $\begin{pmatrix}0 & 0 \ 0&0 \end{pmatrix}$?
A1: No other matrix can be similar to the zero matrix.
A2: $\begin{pmatrix}1 & 0 \ 0 & 0 \end{pmatrix}$
A3: $\begin{pmatrix}0 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{pmatrix}$
A4: $\begin{pmatrix}1 & 0 \ 0 & 1 \end{pmatrix}$
Q2: Let $A$, $B$ similar matrices. What is a correct implication?
A1: $A$ and $B$ are equivalent matrices.
A2: $A-B$ is the identity matrix.
A3: $AB$ is the zero matrix.
A4: $A$ and $B$ are diagonal matrices.
Q3: Are the matrices $\begin{pmatrix} 1 & 0 \ 0 & 2 \end{pmatrix}$ and $\begin{pmatrix} 2 & 0 \ 0 & 1 \end{pmatrix}$ similar?
A1: Yes!
A2: No, they are not even equivalent.
A3: No, but they are equivalent because they have the same rank.
A4: One needs more information.
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Last update: 2024-10