Question

Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. Choose the correct answer below. A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column. B. The system is consistent because all the columns in the augmented matrix will have a pivot position. C. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix. D. The system is consistent because the augmented matrix will cont

Answer 1

Answer: A.

The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

Explanation: a system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column. Since every column of the coefficient matrix is a pivot column, none of the leading coefficients are in the rightmost column of the augmented matrix. Therefore the rightmost column of the augmented matrix cannot be a pivot column and the system must be consistent.