• Title: Linear Subspaces

  • Series: Abstract Linear Algebra

  • YouTube-Title: Abstract Linear Algebra 3 | Linear Subspaces

  • Bright video: https://youtu.be/Ek5Ebm6t6nY

  • Dark video: https://youtu.be/d77TOcT_Eeo

  • Quiz: Test your knowledge

  • PDF: Download PDF version of the bright video

  • Print-PDF: Download printable PDF version

  • Thumbnail (bright): Download PNG

  • Thumbnail (dark): Download PNG

  • Subtitle on GitHub: ala03_sub_eng.srt missing

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

    Q1: Let $V$ be a vector space with zero vector $\mathbf{o}$. Which claim is correct?

    A1: $0 \cdot v = \mathbf{o}$ for all $v \in V$.

    A2: $(-1) \cdot v = \mathbf{o}$ for all $v \in V$.

    A3: $\lambda \cdot v = \mathbf{o}$ for all $v \in V$ and all $\lambda \in \mathbb{F}$.

    A4: $(-1) \cdot v + v = v$ for all $v \in V$.

    Q2: Let $V$ be a vector space and $U \subseteq V$ a subspace. What is not correct in general?

    A1: $u + v \in U$ for each $u \in U$ and $v \in V$.

    A2: $u + v \in U$ for all $u,v \in U$.

    A3: $\lambda \cdot u \in U$ for all $ u \in U$ and all $\lambda \in \mathbb{F}$.

    A4: The zero vector lies in $U$.

  • Back to overview page