• Title: Equivalent Matrices

  • Series: Abstract Linear Algebra

  • YouTube-Title: Abstract Linear Algebra 28 | Equivalent Matrices

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

  • Dark video: https://youtu.be/a0X6ac1Jow4

  • Quiz: Test your knowledge

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  • Subtitle on GitHub: ala28_sub_eng.srt missing

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  • Quiz Content

    Q1: Which of the followig matrices is equivalent to the zero matrix $\begin{pmatrix}0 & 0 \ 0&0 \end{pmatrix}$?

    A1: No other matrix can be equivalent to the zero matrix.

    A2: $\begin{pmatrix}1 & 0 \ 0 & 0 \end{pmatrix}$

    A3: $\begin{pmatrix}0 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{pmatrix}$

    A4: $\begin{pmatrix}1 & 0 \ 0 & 1 \end{pmatrix}$

    Q2: Let $A$, $B$ equivalent matrices. What is a correct implication?

    A1: There are invertible matrices $S,T$ such that $ SA = B T$

    A2: There is an invertible matrix $T$ such that $ A = T^{-1} B T$

    A3: $AB$ is the zero matrix.

    A4: $A$ and $B$ are diagonal matrices.

    A5: $A,B$ are square matrices.

    Q3: Are the matrices $A = \begin{pmatrix} 1 & 0 \ 0 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \ 2 & 2 \end{pmatrix}$ equivalent?

    A1: Yes!

    A2: No!

    A4: One needs more information.

  • Last update: 2024-10

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