3.7-06 Reusing a factorization

Reusing a factorization — linear algebra practice

Plan repeated linear solves when the coefficient matrix stays fixed. Identify the reusable work, process several targets as a matrix, compare factorization and substitution costs and retain a saved permutation consistently. The set also distinguishes harmless target changes from changes that invalidate the factors.

What you will practise

• Identify valid factor reuse
• Solve multiple right-hand sides
• Compare work and preserve pivot conventions

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 LU or pivoted LU and substitution. 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 choose an efficient workflow for repeated systems.