Be careful copying each exercise - you are responsible for copy errors. Good luck!! 1. True or False - Use the full word and explain why it is true or false. a) Let A be an m x n matrix, and assume m>n. Additionally, assume that the matrix A has n pivots. Then for any vector b € R", the equation Ax = b is consistent. b) If for some matrix A, and some vectors x, and b, we have Ax-b consistent, then b is a linear combination of the column vectors of A. c) Let A be an m x n matrix. Then, the homogeneous equation Ax=0 is consistent if and only if the augmented matrix [A 0] has a pivot in every row. d) If the columns of an m x n matrix A span R", then the equation Ax b is consistent for all b in R". e) A non-trivial solution for a homogeneous system may not contain zeros.