Answer
a. False
b. False
c. True
d. True
e. False
Work Step by Step
a. False (The reduced echelon form one obtains from a matrix is unique, page 13.)
b. False (The algorithm applies to any matrix, whether or not the matrix is viewed as an augmented matrix for a linear system, page 12.)
c. True (explanation on page 18.)
d. True (explanation on page 19.)
e. False. (The row [0 0 0 5 0] means that $5x_{4} = 0$ or $x_{4} = $0. If we instead had the a row [0 0 0 0 5] in an echelon form, then this would make the linear system inconsistent because it implies that 0 = 5, a contradiction.)
