3.4-01 Adding and scaling matrices

Adding and scaling matrices — linear algebra practice

Interpret matrix sums and scalar multiples as operations on maps sharing a domain and codomain. Practice entrywise arithmetic and matrix equations while distinguishing addition from composition. Valid distributive rules and additive cancellation are justified with the appropriate shape conditions.

What you will practise

• Check addition dimensions
• Compute linear combinations of matrices
• Interpret pointwise map operations

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 matrix entries and linear maps. 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 combine transformations without confusing operation types.