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Title: Distributions Form a Vector Space
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Series: Distributions
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YouTube-Title: Distributions 7 | Distributions Form a Vector Space
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Bright video: https://youtu.be/EzUaKFGEvqY
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Dark video: https://youtu.be/_dTQGnFd8Xk
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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: dt07_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: What is correct for the distribution $T = 2 \cdot \delta$?
A1: $T(\varphi) = \varphi(0)$
A2: $T(\varphi) = 3 \cdot \varphi(0)$
A3: $T(\varphi) = 2 \cdot \varphi(0)$
A4: $T(\varphi) = \frac{1}{2} \cdot \varphi(0)$
Q2: What is correct for the distribution $T = 2 \cdot \delta + 3 \cdot T_f$ with a locally integrable function $f$?
A1: $T(\varphi) = 2 \cdot \varphi(0)$
A2: $T(\varphi) = 2 \cdot \varphi(0) + \int_{\mathbb{R}^n} f(x) \varphi(x) dx $
A3: $T(\varphi) = 2\varphi(0) + 3\int_{\mathbb{R}^n} f(x) \varphi(x) dx $
Q3: Consider the duality pairing $\langle \cdot, \cdot \rangle$. What is a correct reformulation? $$\langle T + 2 S, \varphi + 3 \psi \rangle = $$
A1: $2 \langle T , \varphi + \psi \rangle$
A2: $2 \langle T-S, \varphi + \psi \rangle$
A3: $\langle T + 2 S, \varphi + 3 \psi \rangle + \langle S, \varphi + 3 \psi \rangle$
A4: $\langle T, \varphi + 3 \psi \rangle + 2\langle S, \varphi \rangle + 6\langle S, \psi \rangle$