In each case either show that the statement is true, or give an example3 showing it is false.
(a) If a linear system has n variables and m equations, then the augmented matrix has n rows.
(b) A consistent linear system must have infinitely many solutions.
(c) If a row operation is done to a consistent linear system, the resulting system must be consistent.
(d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.
(e) If A is row equivalent to B and B is row equivalent to C, then A is row equivalent to C.