Page 629 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let us choose to be the basis for and choose (17)
to be the basis for . We showed in Examples

Example 1 and Example 6 that

Thus it follows from 17 that

As a check, we will calculate directly from Formula 4. Since (18)
and that , it follows from Formula 4 with

(19)

Using 16 yields

Since , it follows from this that

Substituting in 19 yields

which agrees with 18.

Exercise Set 8.4

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