The matrices are all n × n. Each part of the exercises is an implication of the form “If ‘statement 1’, then ‘statement 2’.” Mark an implication as True if the truth of “statement 2” always follows whenever “statement 1” happens to be true. An implication is False if there is an instance in which “statement 2” is false but “statement 1” is true. Justify each answer.

(T/F) If A is an n x n matrix, then the equation Ax = b has at least one solution for each b in Rⁿ.