Scaling Matrix and Linear Transformation

This GeoGebra applet demonstrates the geometric effects of scaling matrices and their inverses on 2D plane figures. By constructing vectors, polygons, and grid lines, it visually illustrates how matrix multiplication scales and transforms geometric shapes. Utilizing the matrix inversion command, it also explores the geometric meaning of inverse transformations, serving as an excellent visualization tool for learning matrix transformations and analytic geometry in linear algebra. Students can dynamically adjust scaling factors and observe how shapes are stretched or compressed along different axes, while the inverse matrix reveals how the transformation can be reversed. The interactive grid lines provide a clear reference framework that helps learners understand coordinate mappings under linear transformations. This hands-on exploration deepens conceptual understanding of key linear algebra topics including eigenvalues, diagonal matrices, and the geometric interpretation of matrix operations.