3.7-03 Solving with LU

Solving with LU — linear algebra practice

Use forward and back substitution to solve systems from an existing factorization. Practice each triangular stage separately before complete two- and three-variable examples. Residual checks return the answer to the original equation, and zero pivots are treated as a prompt to analyze consistency and freedom.

What you will practise

• Perform both substitution stages
• Solve complete factored systems
• Verify residuals and diagnose zero pivots

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 triangular equations. 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 reuse factors across several targets.