-
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
-
Ad-free video: Watch Vimeo video
-
Forum: Ask a question in Mattermost
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Exercise Download PDF sheets
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: la17_sub_eng.srt missing
-
Download bright video: Link on Vimeo
-
Download dark video: Link on Vimeo
-
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
