3.3-04 Designing maps with prescribed behavior

Designing maps with prescribed behavior — linear algebra practice

Construct maps that are injective, surjective, bijective or neither. Start with coordinate embeddings and projections, then modify identity matrices, select parameter values and prescribe an erased line. Impossible specifications are diagnosed from dimensions rather than addressed with arbitrary coefficient choices.

What you will practise

• Build examples and counterexamples
• Modify matrices while tracking behavior
• Recognize impossible design requirements

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 pivot criteria and dimension constraints. 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 use map structure in matrix algebra.