In parts (a) through (e) below, mark the statement True or False. Justify each answer. (a) In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. Is this statement true or false? O A. The statement is false. For each matrix, there is only one sequence of row operations that row reduces it. O B. The statement is true. It is possible for there to be several different sequences of row operations that row reduces a matrix. C. The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might not be unique. O D. The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix. (b) The row reduction algorithm applies only to augmented matrices a linear system. Is this statement true or false? O A. The statement is false. It is possible to create a linear system such that the row reduction algorithm does not apply to the corresponding augmented matrix. O B. The statement is false. The algorithm applies to any matrix, whether or not the matrix is viewed as an augmented matrix for a linear system. OC. The statement is true. The row reduction algorithm is only useful when it is used to find the solution of a linear system. O D. The statement is true. Every matrix with at least two columns can be interpreted as the augmented matrix of a linear system. (c) A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix. Is this statement true or false? O A. The statement is true. If a linear system has both basic and free variables, then each basic variable can be expressed in terms of the free variables. O B. The statement is false. Not every linear system has basic variables. O C. The statement is false. A variable that corresponds to a pivot column in the coefficient matrix is called a free variable, not a basic variable. O D. The statement is true. It is the definition of a basic variable. (d) Finding a parametric description of the solution set of a linear system is the same as solving the system. Is this statement true or false? O A. The statement is false. The solution set of a linear system can only be expressed using a parametric description if the system has at least one solution. O B. The statement is false. The solution set of a linear system can only be expressed using a parametric description if the system has no more than one solution. O C. The statement is true. Solving a linear system is the same as finding the solution set of the system. The solution set of a linear system can always be expressed using a parametric description. O D. The statement is true. Regardless of whether a linear system has free variables, the solution set of the system can be expressed using a parametric description. (e) If one row in an echelon form of an augmented matrix is [ 0 0 0 5 0 ,then the associated linear system is inconsistent. Is this statement true or false? O A. The statement is false. The indicated row corresponds to the equation 5x4 = 0, which does not by itself make the system inconsistent. O B. The statement is true. The indicated row corresponds to the equation 5 = 0. This equation is a contradiction, so the linear system is inconsistent. OC. The statement is true. The indicated row corresponds to the equation 5x4 = 0. This equation is not a contradiction, so the linear system is inconsistent. O D. The statement is false. The indicated row corresponds to the equation 5x4 = 0, which means the system is consistent.