Page 623 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Solution

From the formula for T,

Expressing these vectors as linear combinations of , , and , we obtain (verify)
Thus

so

EXAMPLE 4 Verifying Formula (5a)
Let be the linear operator defined by

and let be the basis, where

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

Solution (a)

From the given formula for T,
Therefore,