Exercises on the four fundamental subspaces
Problem 10.1: (3.6 #11. Introduction to Linear Algebra: Strang) A is an m by n matrix of rank r. Suppose there are right sides b for which Ax = b has no solution.
a) What are all the inequalities (< or ≤) that must be true between m, n, and r?
b) How do you know that ATy = 0 has solutions other than y = 0?
Problem 10.2: (3.6 #24.) ATy = d is solvable when d is in which of the four subspaces? The solution y is unique when the contains only the zero vector.
