A and B are n x n matrices. Check the true statements below: 000ОС A. det AT = (-1)det A. B. det(A + B) = det A + detB. C. If the columns of A are linearly dependent, then det A = 0. D. The determinant of A is the product of the diagonal entries in A. E. If det A is zero, then two rows or two columns are the same, or a row or a column is zero.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 15CR
icon
Related questions
Question
A and B are n x n matrices.
Check the true statements below:
A. det AT = (-1)det A.
B. det(A + B) = det A + detB.
C. If the columns of A are linearly dependent, then det A = 0.
D. The determinant of A is the product of the diagonal entries in A.
E. If det A is zero, then two rows or two columns are the same, or a row or a column is zero.
Transcribed Image Text:A and B are n x n matrices. Check the true statements below: A. det AT = (-1)det A. B. det(A + B) = det A + detB. C. If the columns of A are linearly dependent, then det A = 0. D. The determinant of A is the product of the diagonal entries in A. E. If det A is zero, then two rows or two columns are the same, or a row or a column is zero.
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning