Prove Theorem 3 as follows: Given an m x n matrix A, an element in Col A

Question:

Prove Theorem 3 as follows: Given an m x n matrix A, an element in Col A has the form Ax for some x in Rn. Let Ax and Aw represent any two vectors in Col A.
a. Explain why the zero vector is in Col A.
b. Show that the vector Ax C Aw is in Col A.
c. Given a scalar c, show that c(Ax) is in Col A.