Page 630 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let be the linear transformation defined by .
1.

(a) Find the matrix for T with respect to the standard bases

where

(b) Verify that the matrix obtained in part (a) satisfies Formula 4a for every vector in .

Let be the linear transformation defined by
2.

(a) Find the matrix for T with respect to the standard bases and for and .

(b) Verify that the matrix obtained in part (a) satisfies Formula 4a for every vector in .

Let be the linear operator defined by
3.

(a) Find the matrix for T with respect to the standard basis for .

(b) Verify that the matrix obtained in part (a) satisfies Formula 5a for every vector in .

Let be the linear operator defined by
4. be the basis for which

and let

(a) Find .
(b) Verify that Formula 5a holds for every vector x in .

Let be defined by
5.