Subjects Linear Algebra

Determinant Echelon Cdc1Cf

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Determinant Echelon Cdc1Cf


1. The problem asks whether the determinant of an $n \times n$ matrix $A$ in echelon form is the product of the elements along its main diagonal. 2. Recall that the determinant of a triangular matrix (upper or lower) is the product of its diagonal elements. 3. A matrix in echelon form is an upper triangular matrix with zeros below the main diagonal. 4. Therefore, the determinant of $A$ is indeed the product of the diagonal elements. 5. Hence, the statement is \textbf{True}.