3.7-04 Permutation matrices

Permutation matrices — linear algebra practice

Represent row exchanges and coordinate cycles with permutation matrices. Use the explicit convention PA=LU throughout, including transformation of the right-hand side. Later questions address swap order, multipliers stored before a later pivot swap and a singular pivoted factorization.

What you will practise

• Construct and invert permutations
• Use PA=LU consistently
• Track later swaps and saved multipliers

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 row exchanges, 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 solve systems with pivoting without convention errors.