• Title: Row Picture

  • Series: Linear Algebra

  • Chapter: Matrices and linear systems

  • YouTube-Title: Linear Algebra 15 | Row Picture

  • Bright video: https://youtu.be/g1qLd_1F10Q

  • Dark video: https://youtu.be/8BPVI2CPSF0

  • 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: la15_sub_eng.srt missing

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

    Q1: Which claim is correct for vectors $\mathbf{u}, \mathbf{v} \in \mathbb{R}^n$?

    A1: $\mathbf{u}^T \mathbf{v} = \langle \mathbf{u}, \mathbf{v} \rangle$

    A2: $\mathbf{u} \mathbf{v}^T = \langle \mathbf{u}, \mathbf{v} \rangle$

    A3: $\mathbf{u} \mathbf{v} = \langle \mathbf{u}, \mathbf{v} \rangle$

    A4: $\mathbf{u}^T \mathbf{v}^T = \langle \mathbf{u}, \mathbf{v} \rangle$

    Q2: Let $\mathbf{u}, \mathbf{v} \in \mathbb{R}^2$ given by $\mathbf{u} = \binom{1}{2}$ and $\mathbf{v} = \binom{-2}{3}$. What is $\mathbf{u}^T \mathbf{v}$?

    A1: $4$

    A2: $0$

    A3: $1$

    A4: $3$

    A5: $2$

    Q3: For a matrix $A$ with rows $\alpha_1^T, \ldots, \alpha_m^T$, we calculate the matrix-vector product $A \mathbf{x}$. What do we get?

    A1: $$\begin{pmatrix} \alpha_1^T \mathbf{x} \ \alpha_2^T \mathbf{x} \ \ldots \ \alpha_m^T \mathbf{x}\end{pmatrix} $$

    A2: $$\begin{pmatrix} \alpha_m^T \mathbf{x} \ \alpha_m^T \mathbf{x} \ \ldots \ \alpha_m^T \mathbf{x}\end{pmatrix} $$

    A3: $$\begin{pmatrix} \alpha_m^T \mathbf{x}^T \ \alpha_m^T \mathbf{x}^T \ \ldots \ \alpha_m^T \mathbf{x}^T \end{pmatrix} $$

    A4: $$\begin{pmatrix} \alpha_1^T \mathbf{x} \ \alpha_1^T \mathbf{x} \ \ldots \ \alpha_1^T \mathbf{x}\end{pmatrix} $$

  • Last update: 2024-10

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