• Title: Solutions for Linear Equations

  • Series: Abstract Linear Algebra

  • YouTube-Title: Abstract Linear Algebra 31 | Solutions for Linear Equations

  • Bright video: https://youtu.be/6O7-QBPYpNo

  • Dark video: https://youtu.be/FQpdLA6lcv0

  • Quiz: Test your knowledge

  • PDF: Download PDF version of the bright video

  • Dark-PDF: Download PDF version of the dark video

  • Print-PDF: Download printable PDF version

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  • Subtitle on GitHub: ala31_sub_eng.srt missing

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  • Subtitle in English (n/a)
  • Quiz Content

    Q1: Let $\ell: V \rightarrow W$ be a linear map. What is correct?

    A1: $\mathrm{Ran}(\ell) \subseteq W$

    A2: $\mathrm{Ran}(\ell) \subseteq V$

    A3: $\mathrm{Ran}(\ell) = V$

    A4: $\mathrm{Ran}(\ell) = W$

    A5: $\mathrm{Ran}(\ell) \in V$

    A6: $\mathrm{Ran}(\ell) \in W$

    Q2: Let $\ell: V \rightarrow W$ be a linear map. What is correct?

    A1: $\mathrm{Ker}(\ell) \subseteq V$

    A2: $\mathrm{Ker}(\ell) \subseteq W$

    A3: $\mathrm{Ker}(\ell) = V$

    A4: $\mathrm{Ker}(\ell) = W$

    A5: $\mathrm{Ker}(\ell) \in V$

    A6: $\mathrm{Ker}(\ell) \in W$

    Q3: Let $\ell: V \rightarrow W$ be a linear map where $\mathrm{dim}(V) = 5$. What is never possible?

    A1: $\mathrm{Ker}(\ell)$ is 4-dimensional and $\mathrm{Ran}(\ell)$ is 2-dimensional.

    A2: $\mathrm{Ker}(\ell)$ is 2-dimensional and $\mathrm{Ran}(\ell)$ is 3-dimensional.

    A3: $\mathrm{Ker}(\ell)$ is 5-dimensional.

    A4: $\mathrm{Ran}(\ell)$ is 5-dimensional.

  • Last update: 2024-10

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