linear algebra problem: determine if the given statements are true or false. justify your answers (i. e., give a proof for true and a counterexample for false).

(a) if a linear system has more equations than variables, then it must be inconsistent.

(b) if a linear system has free variables, then it must have infinitely many solutions.

(c) every linear system with the same number of equations and variables has a unique solution.

(d) in every linear system with 2 equations and 3 variables x1,x2,x3, the last variable x3 is a free variable.

(e) if x1 = x2 = ··· = xn = 0 is a solution to a linear system, then the system must be homogeneous.