Problem 1

Row reduce the matrices to reduced echelon form. Box the pivot positions in the final matrix and in the original matrix, and list the pivot columns.

(a).

The pivot columns are 1, 2, and 4

Problem 2

Suppose each matrix represents the augmented matrix for a system of linear equations where represents a pivot position an represents any arbitrary number (zero or nonzero).. In each case, determine if the system is consistent. If the system is consistent, determine if the solution is unique.

(a).

The system is consistent and has only one solution.

(b).

The system is consistent and has infinitely many solutions as row column 2 has no pivot position.

Problem 3

Mark each statement True or False.

• [ ] 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.
• [x] Reducing a matrix to echelon form is called the forward phase of the row reduction process.