Mark each statement True or False. Justify each answer. a. A row replacement operation does not affect the determinant of a

Question

Mark each statement True or False. Justify each answer.

a. A row replacement operation does not affect the determinant of a matrix.

b. 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.

c. If the columns of A are linearly dependent, then det A = 0.

d. det(A + B) = det A + det B.

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