3.8-01 Affine versus linear maps

Affine versus linear maps — linear algebra practice

Separate a linear transformation from a fixed translation term. Classify formulas, track points and displacement vectors, and examine midpoint preservation, composition and inversion. These comparisons show which linearity identities survive for affine maps and which require an origin-fixing condition.

What you will practise

• Classify affine formulas
• Transform differences and midpoints
• Compose and invert affine maps

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review linear maps, matrix products and inverses. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to represent translation with homogeneous coordinates.