Choose an inner product on R2 from the list in Exercise 7.5.1, and an inner product on

Question:

Choose an inner product on R2 from the list in Exercise 7.5.1, and an inner product on R3 from the list in Exercise 7.5.3, and then compute the adjoint of

Exercise 7.5.1
Choose one from the following list of inner products on R2. Then find the adjoint of

when your inner product is used on both its domain and target space.
(a) The Euclidean dot product
(b) The weighted inner product
(v, w) = 2v1 w1 + 3v1 w1
(c) The inner product (v, w) = vT K w defined by the positive definite matrix

Exercise 7.5.3
Choose one from the following list of inner products on R3 for both the domain and target space, and find the adjoint of

(a) The Euclidean dot product on R3
(b) The weighted inner product
(v, w) = v1w1 + 2v2w2 + 3v3w3
(c) The inner product (v, w) = vT K w defined by the positive definite matrix