Learn how to change coordinate systems to find the transformation matrix with respect to standard coordinates in this 29-minute video lesson on linear algebra. Explore the concept of changing coordinate systems as a method to simplify the process of finding transformation matrices. Delve into advanced mathematical reasoning that extends beyond two dimensions, providing a foundation for understanding multi-dimensional concepts. Part of Khan Academy's comprehensive linear algebra course, this video builds upon previous lessons and prepares you for future topics such as orthonormal bases. Gain valuable insights into matrices, vectors, vector spaces, and transformations that are essential for science and engineering applications.