Page 622 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

By inspection, we can determine the coordinate vectors for and relative to ; they are
Thus the matrix for T with respect to B and is

EXAMPLE 2 Verifying Formula (4a)
Let be the linear transformation in Example 1. Show that the matrix

(obtained in Example 1) satisfies 4a for every vector in .

Solution , we have

Since

For the bases B and in Example 1, it follows by inspection that

Thus

so 4a holds.

EXAMPLE 3 Matrix for a Linear Transformation for and for , where
Let be the linear transformation defined by

Find the matrix for the transformation T with respect to the bases