Since the columns span , we have a pivot in every row. Since the matrix is a square matrix, it must also have a pivot in every column. Consequently, the columns are linearly independent. For each of the following maps, determine if it is a linear transformation. If it is, find its standard matrix.
T is the map from to defined by .
T is the map from to defined by . Take for example and . T is the map from to which is the composition of reflection with respect to the -axis followed by the rotation of the plane 90 degrees counterclockwise. A linear transformation.