Khan Academy: Linear Algebra: Change Bases to Help Find a Transformation Matrix

Video showing how to change coordinate systems to make finding the transformation matrix with respect to the standard basis easier. First, a specific linear transformation is defined and the regular method for constructing the transformation matrix with respect to the standard basis is reviewed. Then, an alternate basis and a transformation matrix with respect to that basis is determined. Using the relationship between transformation matrices with respect to the standard basis and with respect to an alternate basis, the transformation matrix with respect to the standard basis is constructed. [28:59]