• Title: Solving Systems of Linear Equations (Introduction)

  • Series: Linear Algebra

  • Chapter: Matrices and linear systems

  • YouTube-Title: Linear Algebra 36 | Solving Systems of Linear Equations (Introduction)

  • Bright video: https://youtu.be/NA9WXj2sYGA

  • Dark video: https://youtu.be/bOirYo1OjD8

  • Quiz: Test your knowledge

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  • Subtitle on GitHub: la36_sub_eng.srt missing

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  • Quiz Content

    Q1: What is the solution set of the linear equation $2x_1 - x_2 = 0$ in $\mathbb{R}^2$?

    A1: ${ \mathbf{x} \in \mathbb{R}^2 \mid 2 x_1 = x_2 } $

    A2: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_1 = 2 x_2 } $

    A3: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_1 = 0 } $

    A4: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_1 = \frac{1}{2}, x_2 = 1 } $

    A5: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_1 = x_2 } $

    Q2: What is the solution set for the system $$ \begin{matrix} x_1 + x_2 = 1 \ x_1 - x_2 = 1 \end{matrix} $$

    A1: $\left{ \begin{pmatrix} 1 \ 0 \end{pmatrix} \right}$

    A2: $\left{ \begin{pmatrix} 0 \ 1 \end{pmatrix} \right}$

    A3: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_1 = 1 } $

    A4: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_2 = 0 } $

    A5: $\emptyset$

    Q3: What is the solution set for the system $$ \begin{matrix} x_1 + 2 x_2 = 0 \ x_1 + 2 x_2 = 1 \end{matrix} $$

    A1: $\emptyset$

    A2: $\left{ \begin{pmatrix} 0 \ 1 \end{pmatrix} \right}$

    A3: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_1 = 1 } $

    A4: ${ \mathbf{x} \in \mathbb{R}^2 \mid x_2 = 0 } $

    A5: $\left{ \begin{pmatrix} \frac{1}{2} \ 1 \end{pmatrix} \right}$

  • Last update: 2024-10

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