3.7-01 Elimination multipliers

Elimination multipliers — linear algebra practice

Recover the lower-triangular factor from the coefficients used during elimination. Track signs, nonunit pivots, negative multipliers and updated entries at later stages. A reconstruction task connects the stored values to the original matrix rather than treating them as bookkeeping alone.

What you will practise

• Compute entry-to-pivot ratios
• Store multipliers with correct signs
• Use updated entries and reconstruct rows

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 Gaussian elimination and elementary matrices. 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 compute LU factorizations reliably.