Mark each statement as true or false Justify your answers In

Mark each statement as true or false. Justify your answers. In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. The row reduction algorithm applies only to augmented matrices for a linear system. A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix. Finding a parametric description of the solution set of a linear system is the same as solving the system. If one row in an echelon form of an augmented matrix is [0 0 0 5 0], then the associated linear system is inconsistent. The echelon form of a matrix is unique. The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. Reducing a matrix to echelon form is called the forward phase of the row reduction process. Whenever a system has free variables, the solution set contains many solutions. A general solution of a system is an explicit description of all solutions of the system. What would you have to know about the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution?

Solution

(A) True

(B) True

(C) True

(D) True

(E) may or may not we need next row to say result

(F) False

(G) False it depends on columns

(H) False

(I) False it depends on rank of linear system

(J) True.