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Title: Inverses of Linear Maps are Linear
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Series: Linear Algebra
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Chapter: Matrices and linear systems
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YouTube-Title: Linear Algebra 31 | Inverses of Linear Maps are Linear
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Bright video: https://youtu.be/u6IrirgCuTw
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Dark video: https://youtu.be/zcf0kmUJMU4
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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: la31_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: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a linear map. Is $f$ invertible?
A1: Yes, it is!
A2: No, there are examples that are not invertible.
A3: No, all linear maps are not invertible.
Q2: Let $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ be a bijective linear map. Is $f^{-1}$ also linear?
A1: Yes, it is.
A2: No, there are counterexamples.
A3: No, never.
A4: Only if $f=0$.
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Last update: 2024-10
