• Title: Properties of the Matrix Product

  • Series: Linear Algebra

  • Chapter: Matrices and linear systems

  • YouTube-Title: Linear Algebra 17 | Properties of the Matrix Product

  • Bright video: https://youtu.be/BqcxYCM19Wo

  • Dark video: https://youtu.be/Q6G3amKjhtQ

  • 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: la17_sub_eng.srt missing

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

    Q1: Let $A,B$ matrices given by $A = \begin{pmatrix} 1 & 2 \ 0 & 1 \end{pmatrix} $ and $B = \begin{pmatrix} 1 & 2 \ 1 & 2 \end{pmatrix}$. What is correct for $AB - BA$?

    A1: $AB - BA \neq \begin{pmatrix} 0 & 0 \ 0 & 0 \end{pmatrix} $

    A2: $AB - BA = \begin{pmatrix} 0 & 0 \ 0 & 0 \end{pmatrix} $

    A3: $AB - BA = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} $

    A4: $AB - BA $ is not well-defined.

    Q2: What is the correct associative law for the matrix multiplication, assuming $A \in \mathbb{R}^{m \times n}$, $B \in \mathbb{R}^{n\times k}$, and $C \in \mathbb{R}^{k \times \ell}$?

    A1: $ (A B) C = A (BC) $

    A2: $ (A + B) C = A C + B C $

    A3: $ (A + B) + C = A C + B C $

    A4: $ (A B ) C = B ( A C) $

    A5: $ A B = BC $

    Q3: Let $A,B$ be matrices where $A$ is given by $A = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$. What is the matrix product $AB$?

    A1: $B$

    A2: $A$

    A3: $\begin{pmatrix} 1 & 1 \ 1 & 1 \end{pmatrix}$

    A4: $A+B$

  • Last update: 2024-10

  • Back to overview page