Question 5 Determine whether the following statements are true for all 2 × 2 matrices A and B. For any of the statements that are false, find a counterexample. (a) det(AB) = det(A) det(B) (b) det(A+B) = det(A) + det (B) (c) det (2A) 2 det(A) = (d) det(-A) = det(A)
Question 5 Determine whether the following statements are true for all 2 × 2 matrices A and B. For any of the statements that are false, find a counterexample. (a) det(AB) = det(A) det(B) (b) det(A+B) = det(A) + det (B) (c) det (2A) 2 det(A) = (d) det(-A) = det(A)
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 11CR
Question
Transcribed Image Text:Question 5
Determine whether the following statements are true for all 2 × 2 matrices A and B. For any of the
statements that are false, find a counterexample.
(a) det(AB) = det(A) det(B)
(b) det(A+B) = det(A) + det (B)
(c) det (2A) 2 det(A)
=
(d) det(-A) = det(A)
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