In the following exercises, mark each statement True or False (T/F). Justify each answer. (T/F) In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. (T/F) The echelon form of a matrix is unique. (T/F) The row reduction algorithm applies only to augmented matrices for a linear system. (T/F) The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. (T/F) A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix. (T/F) Reducing a matrix to echelon form is called the forward phase of the row reduction process. (T/F) Finding a parametric description of the solution set of a linear system is the same as solving the system. (T/F) Whenever a system has free variables, the solution set contains a unique solution. (T/F) If one row in an echelon form of an augmented matrix is [00005], then the associated linear system is inconsistent. (T/F) A general solution of a system is an explicit description of all solutions of the system
In the following exercises, mark each statement True or False (T/F). Justify each answer.
(T/F) In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations.
(T/F) The echelon form of a matrix is unique.
(T/F) The row reduction algorithm applies only to augmented matrices for a linear system.
(T/F) The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process.
(T/F) A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix.
(T/F) Reducing a matrix to echelon form is called the forward phase of the row reduction process.
(T/F) Finding a parametric description of the solution set of a linear system is the same as solving the system.
(T/F) Whenever a system has free variables, the solution set contains a unique solution.
(T/F) If one row in an echelon form of an augmented matrix is [00005], then the associated linear system is inconsistent.
(T/F) A general solution of a system is an explicit description of all solutions of the system.
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