Images of F: Matrix Transformations

① This GeoGebra example dynamically demonstrates the image of a geometric figure F (composed of polygons and line segments) under a matrix transformation, visually showing how linear transformations affect geometric objects. ② Core mathematical concepts include matrix multiplication, linear transformations, similarity transformations, vectors, polygons, and the correspondence between original and transformed points, shapes, and orientations. ③ Construction highlights: using commands such as Intersect, Vector, Polygon, ApplyMatrix, Line, and Sequence, the original objects (A, B, u, C, v, m1, D through M, poly1, and segments d through m) are constructed, and ApplyMatrix generates the transformed points D' through M', polygon poly1', and segments d' through e', enabling clear comparison between the preimage and image. ④ Suitable for high school or early college students learning linear algebra and geometric transformations, and for teachers to demonstrate the geometric meaning of matrices in class, helping students understand how matrix multiplication acts on planar figures.