3Blue1Brown: 3D Transformations - Chapter 5 Quiz

This quiz reviews three-dimensional linear transformations from Chapter 5 of 3Blue1Brown’s Essence of Linear Algebra. It connects the geometry of transformed space with the entries and columns of a 3 × 3 matrix.

Topics include images of the standard basis vectors, matrix–vector multiplication, axis rotations, scaling, reflection, orthogonal projection, and the identity and zero transformations. Questions also explore how linear maps affect the origin and equally spaced points, including maps that collapse dimensions. Rotation questions require attention to the stated axis, viewing direction, and right-hand convention.

The composition exercises use column vectors and ask you to connect the order of operations with matrix products. You will also consider why following basis vectors simplifies three-dimensional visualization and how these ideas relate to computer graphics and robotics.

Before starting, review coordinates in three dimensions, linear combinations, and basic matrix multiplication. Work out the images of the basis vectors or trace a general input vector to check your reasoning. The explanations support revision after each attempt and distinguish geometric intuition from the algebraic calculation.