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Check the true statements below: ✓A. If the columns of A are linearly dependent, then detA=0. B. det(A + B) = det A + det.B. ✓C. 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. ✓D. Adding a multiple of one row to another does not affect the determinant of a matrix.

Check the true statements below: ✓A. If the columns of A are linearly dependent, then detA=0. B. det(A + B) = det A + det.B. ✓C. 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. ✓D. Adding a multiple of one row to another does not affect the determinant of a matrix.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Check the true statements below: ✓A. If the columns of A are linearly dependent, then detA=0. B. det(A + B) = det A + det.B. ✓C. 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. ✓D. Adding a multiple of one row to another does not affect the determinant of a matrix.
Transcribed Image Text:Check the true statements below: ✓A. If the columns of A are linearly dependent, then detA=0. B. det(A + B) = det A + det.B. ✓C. 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. ✓D. Adding a multiple of one row to another does not affect the determinant of a matrix.
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