In each case either show that the statement is true, or give an example showing that it is false.
(a) If AX has a zero entry, then A has a row of zeros.
(b) Every linear combination of vectors in Rn can be written in the form AX.
(c) If A = [A1 A2 A3] in terms of its columns, and if the system AX = B has a solution, then B = sA1 + tA2 for some s, t.
(d) If AX = B has a solution for some column B, then it has a solution for every column B.