A ∈ Rnn which of the following is true? a) If A is regular, the inverse of A can be found with the Cayley-Hamilton theorem. b) < , > is an inner product in Rn1 and u, v ∈ Rn1 and = . c) Rn1 is the direct sum of the eigenspaces obtained versus the eigenvalues of A. d) The characteristic polynomial of A divides the minimal polynomial. e) If L linear transformation has inverse and its matrix is A, then L-1 linear transformation has matrix A as well.
A ∈ Rnn which of the following is true? a) If A is regular, the inverse of A can be found with the Cayley-Hamilton theorem. b) < , > is an inner product in Rn1 and u, v ∈ Rn1 and = . c) Rn1 is the direct sum of the eigenspaces obtained versus the eigenvalues of A. d) The characteristic polynomial of A divides the minimal polynomial. e) If L linear transformation has inverse and its matrix is A, then L-1 linear transformation has matrix A as well.
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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A ∈ Rnn which of the following is true?
a) If A is regular, the inverse of A can be found with the Cayley-Hamilton theorem.
b) < , > is an inner product in Rn1 and u, v ∈ Rn1 and <Au,v> = <u,Av>.
c) Rn1 is the direct sum of the eigenspaces obtained versus the eigenvalues of A.
d) The characteristic polynomial of A divides the minimal polynomial.
e) If L linear transformation has inverse and its matrix is A, then L-1 linear transformation has matrix A as well.
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