Khan Academy: Linear Algebra: Determining Whether a Transformation Is Onto

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 co-domain. Uses this to show that a transformation is onto if and only if the rank of the transformation matrix is equal to the number of columns in the transformation matrix. Gives example of determining if a transformation is onto. [25:51]