Indicate whether the statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample.
(a) If a matrix is reduced to reduced row-echelon form by two different sequences of elementary row operations, the resulting matrices will be different.
(b) If a matrix is reduced to row-echelon form by two different sequences of elementary row operations, the resulting matrices might be different.
(c) If the reduced row-echelon form of the augmented matrix for a linear system has a row of zeros, then the system must have infinitely many solutions.
(d) If three lines in the xy-plane are sides of a triangle, then the system of equations formed from their equations has three solutions, one corresponding to each vertex.