3.1-05 Reading transformed grids

Reading transformed grids — linear algebra practice

Use repeated grid steps, basis arrows and line directions to understand linear transformations geometrically. Follow unit-square vertices and midpoints, distinguish straight-line images from collapsed points, and predict which directions disappear. The final tasks include an offset line whose image must be interpreted carefully.

What you will practise

• Predict repeated displacements
• Track vertices and midpoints
• Identify collapsed directions and line images

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 coordinate geometry and linearity. 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 connect transformed grids with matrix columns.