3.5-04 Elementary matrices

Elementary matrices — linear algebra practice

Encode each elementary row operation as left multiplication by a modified identity. Compare row and column actions, track operation order and identify inverse operations. Examples include swaps, nonzero scaling, row replacement and three-row matrices.

What you will practise

• Construct elementary matrices
• Apply and reverse row operations
• Track multiplication side and sequence

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 elementary row operations and matrix products. 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 justify elimination and inversion algebraically.