Suppose A is a 5 by 3 matrix and Ax is never zero (except when x = 0). (a) What can you say about the columns of A? (b) Show that ATAX is also never zero (except when x = 0) by explaining this key...

Extracted text: Suppose A is a 5 by 3 matrix and Ax is never zero (except when x = 0). (a) What can you say about the columns of A? (b) Show that ATAX is also never zero (except when x = 0) by explaining this key step: If AT Ax = 0 then obviously x" AT Ax = 0 and then (WHY?) Ax = 0. (c) Given that AT A is invertible. (i) Explain why B = (AT A)-1AT is a one-sided inverse of A (which side of A?). (ii) Explain why B is NOT a 2-sided inverse of A.