Multiplying Lines Using Matrices: A Geometric Visualization

① This example demonstrates how multiplying two lines (represented as vectors) using matrices produces new geometric objects, visually linking matrix multiplication to linear transformations. ② Core mathematical concepts include matrix multiplication, linear transformations, line equations, and vector representation. ③ Construction uses GeoGebra commands such as Segment, Element, and LaTeX, with objects including points A, B, C, D, lines f and g, and derived points M, N, P, Q, plus text objects (text1 to text7) displaying formulas. ④ Suitable for high school or early college students learning linear algebra and analytic geometry, and for teachers demonstrating matrix operations in class or for self-study.