Question 1. True or False: In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations.
Answer: False. The reduced row echelon form is unique.
Question 2. The row reduction algorithm applies only to augmented matrices for a linear system.
Answer: False. Any matrix can be reduced. The matrix does not know where it came from.
Question 3. A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix.
Answer: True.
Question 4. Finding a parametric description of the solution set of a linear system is the same as solving the system.
Answer: True.
Question 5. If one row in an echelon form of an augmented matrix is [0 0 0 5 0], then the associated linear system is inconsistent.
Answer: False. This row says 5x_4 = 0, so the variable x_4 = 0.
Question 6. The echelon form of a matrix is unique.
Answer: False. The reduced echelon form is unique.
Question 7. A general solution of a system is an explicit description of all solutions of the system.
Answer: True