Find such that is equal to

- ;
- ;
- ;
- ,

where and denote the unit coordinate vectors and , respectively.

- We can use Theorem 12.9 (page 465 of Apostol) to compute the scalars. In this case we have corresponding to , corresponding to and corresponding to .
Therefore, .

- We can use Theorem 12.9 (page 465 of Apostol) to compute the scalars. In this case we have corresponding to , corresponding to and corresponding to .
Therefore, and .

- We can use Theorem 12.9 (page 465 of Apostol) to compute the scalars. In this case we have corresponding to , corresponding to and corresponding to .
Therefore, and .

- We can use Theorem 12.9 (page 465 of Apostol) to compute the scalars. In this case we have corresponding to , corresponding to and corresponding to .
Therefore, and .