Linear Transformation Matrix Visualization: From Geometry to Matrix Operations

① This GeoGebra example dynamically demonstrates how a linear transformation matrix acts on a plane figure (such as a quadrilateral), visually showing how matrix multiplication changes point positions and shape. ② Core mathematical concepts include matrix multiplication, linear transformations (rotation, scaling, shearing), vector coordinate mapping, and the correspondence between original and transformed figures, along with the algebraic representation of geometric transformations via matrices. ③ Construction highlights: using GeoGebra commands such as Intersect, Vector, Point, OrthogonalLine, and Sequence, with objects A, B, O, u, v, T, C, f, D, E, and images pic1, pic2, pic3; sliders SX and SY control transformation parameters, allowing dynamic adjustment of matrix entries and real-time updates of the transformed figure. ④ Suitable for high school to early college students learning linear algebra or analytic geometry, and for teachers demonstrating the geometric meaning of matrix transformations in class, helping students bridge abstract matrices with visual intuition.