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A and B aren x n matrices. Check the true statements below: O A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)", wherer is the number of row interchanges made during row reduction from A to U. OB. If the columns of A are linearly dependent, then det A = 0. OC. Adding a multiple of one row to another does not affect the determinant of a matrix. OD. det(A + B) = det A + det B.

A and B aren x n matrices. Check the true statements below: O A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)", wherer is the number of row interchanges made during row reduction from A to U. OB. If the columns of A are linearly dependent, then det A = 0. OC. Adding a multiple of one row to another does not affect the determinant of a matrix. OD. det(A + B) = det A + det B.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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A and B aren x n matrices. Check the true statements below: O A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)", where r is the number of row interchanges made during row reduction from A to U. O B. If the columns of A are linearly dependent, then det A = 0. OC. Adding a multiple of one row to another does not affect the determinant of a matrix. OD. det(A + B) = det A + det B.
Transcribed Image Text:A and B aren x n matrices. Check the true statements below: O A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)", where r is the number of row interchanges made during row reduction from A to U. O B. If the columns of A are linearly dependent, then det A = 0. OC. Adding a multiple of one row to another does not affect the determinant of a matrix. OD. det(A + B) = det A + det B.
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