(a) Determine whether the vectors are linearly independent or linearly dependent. (b) Do they form a basis...

Question:

(a) Determine whether the vectors

are linearly independent or linearly dependent.
(b) Do they form a basis of C3?
(c) Compute the Hermitian norm of each vector.
(d) Compute the Hermitian dot products between all different pairs. Which vectors are orthogonal?
(e) Do the vectors form an orthogonal or orthonormal basis of C3?