Prove parts (b) and (c) of Theorem 2.21. Theorem 2.21 (b) The vectors are linearly independent if

Question:

Prove parts (b) and (c) of Theorem 2.21.
Theorem 2.21
(b) The vectors are linearly independent if and only if the only solution to the homogeneous system Ac = 0 is the trivial one, c = 0.
(c) A vector b lies in the span of v1,..., vk if and only if the linear system Ac = b is compatible, i.e., has at least one solution.