3.2-07 Shears

Shears — linear algebra practice

Build horizontal and vertical shear matrices by following basis directions. Calculate shifts, recover a shear parameter and inspect the image of a square. Fixed axes, changing lengths and angles, reversal of a shear, and repeated shears provide geometric meaning beyond entry-by-entry calculation.

What you will practise

• Distinguish horizontal and vertical shears
• Recover parameters from point images
• Analyze fixed directions and compositions

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 standard matrices and plane coordinates. 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 compare transformation order geometrically.