Let S = {v1, v2,..., vk} be an orthonormal basis for the Euclidean space V and {a1,

Question:

Let S = {v1, v2,..., vk} be an orthonormal basis for the Euclidean space V and {a1, a2,..., ak) be any set of scalars none of which is zero. Prove that
T = {a1v1,a2v2, ...,akvk}
is an orthogonal basis for V. How should the scalars a1, a2,..., ak be chosen so that T is an orthonormal basis for V?