-
Title: Linear maps induce matrices
-
Series: Linear Algebra
-
Chapter: Matrices and linear systems
-
YouTube-Title: Linear Algebra 20 | Linear maps induce matrices
-
Bright video: https://youtu.be/9UcgdR_X2Ys
-
Dark video: https://youtu.be/jZqb1RwbCCw
-
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
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: la20_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 $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be a linear map given by $$f(x,y) = \begin{pmatrix} 2y + 3 x \ 5 x - y \end{pmatrix}$$ What is the corresponding matrix $A$ such that $$f(x,y) = A \binom{x}{y}$$ holds?
A1: $$ A = \begin{pmatrix} 3 & 2 \ 5 & -1 \end{pmatrix} $$
A2: $$ A = \begin{pmatrix} 3 & -2 \ -5 & -1 \end{pmatrix} $$.
A3: $$ A = \begin{pmatrix} 2 & 3 \ 5 & -1 \end{pmatrix} $$
A4: $$ A = \begin{pmatrix} 2 & 3 \ 5 & 1 \end{pmatrix} $$
Q2: Let $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be a linear map. Is it possible that $f_A = f_B$ for different matrices $A,B \in \mathbb{R}^{2 \times 2}$.
A1: No, never.
A2: Yes, always.
A3: Only if $f = 0$.
Q3: Let $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be a linear map. What is the first column of the matrix $A$ such that $f = f_A$?
A1: $f(e_1)$
A2: $f(e_2)$
A3: $f(e_1 + e_2)$
A4: One needs more information.
-
Last update: 2024-10
