3Blue1Brown: Vectors | Essence of Linear Algebra - Chapter 1 Quiz

This quiz assesses your understanding of the foundational concepts of vectors as introduced in 3Blue1Brown's 'Vectors | Chapter 1, Essence of linear algebra' video. It covers the three distinct perspectives on vectors (physics, computer science, mathematician), 3Blue1Brown's preferred initial geometric view (arrows rooted at the origin in a coordinate system), the interpretation of vector coordinates, and the two fundamental vector operations: addition (geometric tip-to-tail and numerical component-wise) and scalar multiplication (geometric scaling and numerical component-wise). The quiz also touches upon the overarching theme of translating between geometric intuition and numerical representation, and the practical applications of these concepts in various fields.

Key formulas covered:

• Vector addition (numerical): $\vec{a} + \vec{b} = \begin{pmatrix} x_1 \\ y_1 \end{pmatrix} + \begin{pmatrix} x_2 \\ y_2 \end{pmatrix} = \begin{pmatrix} x_1+x_2 \\ y_1+y_2 \end{pmatrix}$
• Scalar multiplication (numerical): $c \vec{v} = c \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} cx \\ cy \end{pmatrix}$

Remember to consider the specific nuances and emphasis presented in the video for each concept.