Let A be an nxn matrix. Determine whether the statement below is true or false.Justify the answer.If A+5 is a factor of the characteristic polynomial of A, then 5 is an eigenvalue of A.The statement is false. If X+5 is a factor of the characteristic polynomial of A,then -5 is an eigenvalue of A. In order for 5 to be an eigenvalue of A, thecharacteristic polynomial would need to have a factor of X-5.The statement is true. IfA+5 is a factor of the characteristic polynomial of A,then X+5 must be an entry on the main diagonal of A-.The statement is false. The factors of the characteristic polynomial are useful fordetermining the eigenvectors of a matrix, not its eigenvalues.The statement is true. If +5 is a factor of the characteristic polynomial of A,then X=5 is a root of the characteristic equation. Let A be an nxn matrix. Determine whether the statement below is true or false.Justify the answer.The multiplicity of a root r of the characteristic equation of A is called the algebraicmultiplicity of r as an eigenvalue of A.The statement is false. The multiplicity of a root r of the characteristic equationof A is the number of eigenvectors corresponding to that root.The statement is true. It is the definition of the multiplicity of a root of thecharacteristic equation of A.The statement is true. It is the definition of the algebraic multiplicity of aneigenvalue of A.OThe statement is false. The multiplicity of a rootr of the characteristic equation.of A is called the geometric multiplicity of r as an eigenvalue of A.

λ +5 is a factor of A. Then its eigen value is λ+5=0 λ = -5

Let A be an nxn matrix. Determine whether the statement below is true c Justify the answer. If A+5 is a factor of the characteristic polynomial of A, then 5 is an eigen The statement is false. If X+5 is a factor of the characteristic polyno then -5 is an eigenvalue of A. In order for 5 to be an eigenvalue of A characteristic polynomial would need to have a factor of X-5. The statement is true. If +5 is a factor of the characteristic polyno then A+5 must be an entry on the main diagonal of A-AI. The statement is false. The factors of the characteristic polynomia determining the eigenvectors of a matrix, not its eigenvalues. O The statement is true. If X+5 is a factor of the characteristic poly then X-5 is a root of the characteristic equation.

Let A be an nxn matrix. Determine whether the statement below is true c Justify the answer. If A+5 is a factor of the characteristic polynomial of A, then 5 is an eigen The statement is false. If X+5 is a factor of the characteristic polyno then -5 is an eigenvalue of A. In order for 5 to be an eigenvalue of A characteristic polynomial would need to have a factor of X-5. The statement is true. If +5 is a factor of the characteristic polyno then A+5 must be an entry on the main diagonal of A-AI. The statement is false. The factors of the characteristic polynomia determining the eigenvectors of a matrix, not its eigenvalues. O The statement is true. If X+5 is a factor of the characteristic poly then X-5 is a root of the characteristic equation.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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