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. 59. (a) A 6 × 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.

Question

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.
59. (a) A 6 × 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.

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