Visualizing Invariant Lines of Matrix {{-2,5},{6,-9}}

This GeoGebra example demonstrates which lines (invariant directions) remain unchanged under the 2D linear transformation defined by the matrix A = {{-2,5},{6,-9}}. In other words, it visualizes the geometric content of eigen-directions by showing directions whose points map onto the same line after applying the matrix. The key mathematics includes linear transformations, eigenvalues/eigenvectors (equivalently, invariant directions), and the mapping of vectors and points under matrix multiplication. Construction-wise, it uses commands such as ApplyMatrix to transform vectors/points by A, Vector to represent direction vectors (e.g., u, v, w), DynamicCoordinates to interactively place elements, ClosestPoint to locate/associate images with nearby candidate geometry, and If to conditionally select configurations. The scene includes objects like M, A, B, C, C' and a labeled text element (text2) to connect original and transformed geometry. Suitable for high-school advanced topics and early undergraduate linear algebra, especially for building intuition about eigenvectors as invariant lines.