Find Standard Matrix of a Linear Transformation
You are being ask to generalize the example from pages 20 and 21 in LADW which considers the. Y x y-x y x. Linear Transformation Standard Matrix The Standard Basis Mathe So one approach would be to solve a system of linear equations to write the vectors of the standard basis in terms of your vectors. . Then there is always a unique matrix A such that. The matrix A such that Tx Ax is given by. Then there exists a unique matrix A called the standard matrix of T such that. Define a linear transformation T. In fact A is the mn matrix whose jth column is the vector Te j with e j 2 IR n. T e n. R 2 R 2 by. The transformation matrix is a representation of the transformed standard basis vectors. The columns of a transformations standard matrix are the the vectors you get when you apply the transformation to the columns of the identity matrix. The standard matrix of a transformation T. U 1 1 ubegin...