linear algebra proof question please show clear thanks Problem 9: What's wrong with the following "proof" of the Cayley-Hamilton the-orem for matrices? (Clearly explain the error involved.)“Let A ¤ Mnxn(F). The characteristic polynomial of A is defined asXA(t) = det(A-t.In).ThenXA (A) = det (A - A.In) = det(A - A) = 0.Hence A satisfies its own characteristic equation."

Cayley-Hamilton theorem : Every square matrix satisfies its own…

Answered: Problem 9: What's wrong with the…

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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linear algebra proof question

please show clear thanks

Problem 9: What's wrong with the following "proof" of the Cayley-Hamilton the-
orem for matrices? (Clearly explain the error involved.)
“Let A ¤ Mnxn(F). The characteristic polynomial of A is defined as
XA(t) = det(A-t.In).
Then
XA (A) = det (A - A.In) = det(A - A) = 0.
Hence A satisfies its own characteristic equation."

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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