3.3-02 Surjectivity and reachable outputs

Surjectivity and reachable outputs — linear algebra practice

View surjectivity as reaching every vector in the declared codomain. Link target equations with column span and row pivots, construct preimages and analyze output constraints. Parameter-dependent maps and the distinction between nonzero rows and independent rows deepen the coverage test.

What you will practise

• Use column span and row pivots
• Describe reachable targets
• Construct general preimages

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 linear systems and matrix column combinations. 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 judge complete output coverage.