An instructional video that explains how the method for finding the inverse transformation matrix is derived. It is the same method for finding the inverse for any invertible matrix. [18:00]

Video reviews from previous videos that a function is invertible if and only if it is onto and one-to-one. Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the...

Video first reviews what the null space is and how to solve for it using reduced row echelon form. Shows that any solution to the inhomogeneous system Ax = b will be the sum of a particular solution and a homogeneous solution. Extends...

A video lesson that gives an in-depth, algebraic proof showing that the inverse of a linear transformation is also linear. [21:25]

A video lesson explaining that a transformation matrix is invertible if and only if it is a square identity matrix in reduced row echelon form. This video is also found in the strand Algebra: Matrices. [6:37]

Video first reviews what the image under a transformation is and then introduces the concept of preimage. [5:23]

Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the co-domain.

A video lesson explaining that a transformation matrix is invertible if and only if it is a square identity matrix in reduced row echelon form.

Showing that inverse transformations are also linear.