Let A, B, and C be matrices of appropriate dimensions such that all following products are defined. a. Prove that tr(ABC) = tr(BCA) = tr(CAB).
Let A, B, and C be matrices of appropriate dimensions such that all following products are defined. a. Prove that tr(ABC) = tr(BCA) = tr(CAB).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 76E
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![Let A, B, and C be matrices of appropriate dimensions such that all following products
are defined.
a. Prove that tr(ABC) = tr(BCA) = tr(CAB).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6e77107-ef1d-4e39-badf-4decafa47f1b%2F7ae2928c-bac1-4ed6-8b32-ad37ba5551e0%2F4agxusl_processed.png&w=3840&q=75)
Transcribed Image Text:Let A, B, and C be matrices of appropriate dimensions such that all following products
are defined.
a. Prove that tr(ABC) = tr(BCA) = tr(CAB).
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