Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample.
(a) A linearly dependent set of vectors in an inner product space cannot be orthonormal.
(b) Every finite-dimensional vector space has an orthonormal basis.
(c) projw u is orthogonal to projw i u in any inner product space.
(d) Every matrix with a nonzero determinant has a QR-decomposition.