3.7-05 LDU factorization

LDU factorization — linear algebra practice

Separate diagonal pivots from an upper-triangular factor to obtain unit triangular factors around a diagonal matrix. Compute normalized factors and full products, analyze nonzero-pivot requirements and order the stages of an LDU solve. Matrix order remains explicit when discussing inversion.

What you will practise

• Normalize an upper factor by rows
• Build and verify LDU
• Solve using lower, diagonal and upper stages

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 factorization and nonzero pivots. 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 interpret elimination as separate triangular and diagonal actions.