1. (5 points) Construct a nonzero matrix A with the required property or state why it is impossible: (a) The column space contains (1,2, 3) and (3, 1,2), and the nullspace contains (1,1,1). (b) The row space contains (1,2, 3) and (3, 1,2), and the nullspace contains (1,1,1). 1 1 0 (C) An: = 1 has a solution and AT 0 = 0 1 0 0 (d) Every row is orthogonal to every column. (e) The sum of the columns is the zero vector, and the sum of the rows is a vector with all 1's