Question

true or false: the determinant of a is the product of the pivots in any echelon form u of a, multiplied by . 1/ r , where r is the number of row interchanges made during row reduction from a to u .

Answer 1

The determinant of a is the product of the pivots in any echelon form u of a, multiplied by 1/r, where r is the number of row interchanges made during row reduction from a to u.

Step-by-step explanation:

True or false: The determinant of a is the product of the pivots in any echelon form u of a, multiplied by 1/r, where r is the number of row interchanges made during row reduction from a to u.

This statement is true. In row reduction, we perform elementary row operations such as interchanging rows. Each row interchange changes the sign of the determinant. If r is the number of row interchanges, then the determinant will be multiplied by (-1)^r.

Since each pivot element is obtained after row reductions and row interchanges, the product of the pivots will also include the effect of row interchanges. Therefore, the statement is true.