1. let A be an m by n matrix
a). Prove that every vector x in R^n can be written in the form of x = p + u, where p is in Row(A) and u is in Null(A).
b). Also, show that if the system Ax=b is consistent then there exists a unique p belongs to Row(A) such that Ap=b.
I am really bad at proofs. Can someone please help me start on this problem and give me some explanations? thank you!