Answer :
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 is False.
Given:
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.
Definition of det A:
det A = (-1)^r * (product of pivots in echelon form) if A is invertible or 0 when A is not invertible.
From definition of det A we can simply say the given statement is false - This can only hold if A is an invertible matrix, but the problem does not state this.
Reduction to an echelon form may also include scaling a row by a nonzero constant, which can change the value of the determinant.
Therefore 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 is False.
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