3.1-02 Additivity

Additivity — linear algebra practice

Study preservation of vector addition through symbolic identities, direct tests and counterexamples. Work with zero inputs, opposite vectors, integer combinations and a rational scaling consequence. Particular attention is given to what a finite set of successful tests does and does not prove.

What you will practise

• Interpret the additivity identity
• Test coordinate maps
• Derive consequences without assuming full linearity

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 vector addition and scalar multiplication. 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 build a complete linearity argument.