• Title: Linear Independence (Examples)

  • Series: Linear Algebra

  • Chapter: Matrices and linear systems

  • YouTube-Title: Linear Algebra 23 | Linear Independence (Examples)

  • Bright video: https://youtu.be/Xdx0ZG7T648

  • Dark video: https://youtu.be/062Iy-pbGug

  • 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

  • Thumbnail (bright): Download PNG

  • Thumbnail (dark): Download PNG

  • Subtitle on GitHub: la23_sub_eng.srt missing

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

    Q1: Is the family $(\mathbf{v})$ consisting of a single vector linearly independent?

    A1: Yes, if $ \mathbf{v} \neq 0$.

    A2: No, never!

    A3: Yes, always!

    A4: Yes, if $ \mathbf{v} = 0$.

    A5: Yes, if $ \mathbf{v} \in \mathbb{R}^2$.

    Q2: Is a family consisting of $(n+1)$-many vectors from $\mathbb{R}^n$ linearly independent?

    A1: Yes, if one vector $ \mathbf{v} \neq 0$.

    A2: No, never!

    A3: Yes, always!

    A4: Yes, if one vector $ \mathbf{v} = 0$.

    A5: Yes, if $n = 2$.

    Q3: Let $(\mathbf{u}, \mathbf{v}, \mathbf{w})$ be a family of vectors in $\mathbb{R}^3$ that are linearly independent. Which claim is not correct?

    A1: $ \mathrm{Span}( \mathbf{u}, \mathbf{v}, \mathbf{w} ) = \mathrm{Span}( \mathbf{u}, \mathbf{w} ) $

    A2: $ \mathrm{Span}( \mathbf{u}, \mathbf{v}, \mathbf{w} ) = \mathrm{Span}( \mathbf{u}, \mathbf{v}, \mathbf{w} , \mathbf{w} ) $

    A3: $ \mathrm{Span}( \mathbf{u}, \mathbf{v}, \mathbf{w} ) = \mathrm{Span}( \mathbf{u}, \mathbf{w} , \mathbf{v} ) $

    A4: $ \mathrm{Span}( \mathbf{u}, \mathbf{v}, \mathbf{w} ) = \mathrm{Span}( \mathbf{u}, \mathbf{v} , \mathbf{w} , \mathbf{0} ) $

    A5: One needs more information.

  • Last update: 2024-10

  • Back to overview page