3.2-03 Scaling and contraction

Scaling and contraction — linear algebra practice

Investigate diagonal maps that stretch, contract, reverse or erase coordinate directions. Compare uniform scaling with axis-dependent behavior, compute transformed vectors, recover scale factors and analyze which vectors keep their length or remain fixed. Zero and negative scale factors are treated explicitly.

What you will practise

• Build diagonal scaling matrices
• Calculate and recover axis factors
• Identify fixed vectors and lost directions

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 coordinates, lengths and standard 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 separate scaling effects from rotations and shears.