(a) Show that if ki and fi are eigenvalues and eigenfunctions of the linear operator A, then...

Question:

(a) Show that if ki and fi are eigenvalues and eigenfunctions of the linear operator A, then cki and fi are eigenvalues and eigenfunctions of cA.
(b) Give an operator whose eigenvalues are 1/2, 3/2, 5/2, . . . .
(c) Give an operator whose eigenvalues are 1, 2, 3,c.