Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample.
(a) ||u + v + w|| ≤ ||u|| + ||v|| + ||w|| for all vectors u, v, and w in an inner product space.
(b) If u is in the row space and the nullspace of a square matrix A, then u = 0
(c) If u is in the row space and the column space of an n × n matrix A, then u = 0