Question

The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. Choose the correct answer below. A. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix. B. The statement is true. The pivot positions in a matrix are determined completely by the positions of the leading entries of each row which are dependent on row interchanges. C. The statement is true. Every pivot position is determined by the positions of the leading entries of a matrix in reduced echelon form. D. The statement is false. The pivot positions in a matrix depend on the location of the pivot column.

Answer 1

Answer: A. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix.

Step-by-step explanation:

A pivot position is simply referred to as a location in a matrix row echelon form that's reduced which equates to leading 1.

From the question, we are given a statement that the pivot positions in a matrix depend on whether row interchanges are used in the row reduction process

It should be noted that the statement is false as the pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix.