• For each of the statements below give either a argument to explain why they are correct, or a counterexample to prove they are false.

(a) If the coefficient matrix of a system of m equations in n unknowns has rank n, then the system has a solution.

(b) If the coefficient matrix of a system of m equations in n unknowns has rank m, then the system has a solution.

(c) If the augmented matrix of a system of m equations in n unknowns has rank m, then the system has a solution.

Justify your answers.