(a) Let A be an m x n matrix, where n,m> 2, and y R" such that Ay = 0. Then the columns of A are linearly dependent. (b) The following matrix has four linearly independent columns: -1 3 250-3-2 419-3 7-654-3 9 0 7 8-6 (c) Let A be a 8 x 4 matrix with four linearly independent rows, and E R. If Ax = 0, then x = 0. (d) Let A be an m x n matrix and b Rm such that the system of equations Ar = b over variables R has a solution. Then there is a solution x = a R" with at most m non-zero coordinates. (e) Let A be an m x n matrix such that that the system of equations Ar = 0 over vari- ables R" has n linearly independent solutions. Then A = 0.