Chapter 1.2, Problem 59E

True or False? In Exercises 59 and 60, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) A $6\times 3$ matrix has six rows.

(b) Every matrix is row-equivalent to a matrix in row- echelon form.

(c) If the row- echelon form of the augmented matrix of a system of linear equations contains the row [1 0 0 0 0], then the original system is inconsistent.

(d) A homogeneous system of four linear equations in six variables has infinitely many solutions.