3.7-02 Computing LU

Computing LU — linear algebra practice

Factor matrices into unit-lower and upper-triangular factors when elimination proceeds without row exchanges. Work through two- and three-dimensional examples, verify products and diagnose zero pivots. Singular factorizations, normalization and uniqueness extend the procedure beyond a routine algorithm.

What you will practise

• Construct L and U
• Verify complete factor identities
• Recognize no-swap limitations and normalization

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 elimination multipliers and triangular 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 solve systems using stored factors.