Chapter 6.1, Problem 20E

In Exercises 19 and 20, all vectors are in ℝⁿ. Mark each statement True or False. Justify each answer.

20.

1. a. u·v − v·u = 0.
2. b. For any scalar c, ||cv|| = c||v||.
3. c. If x is orthogonal to every vector in a subspace W, then x is in W^⊥.
4. d. If ||u||² + ||v||² = ||u + v||², then u and v are orthogonal.
5. e. For an m × m matrix A, vectors in the null space of A are orthogonal to vectors in the row space of A.