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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Question

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, the
characteristic 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 for
determining 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 algebraic
multiplicity of r as an eigenvalue of A.
The statement is false. The multiplicity of a root r of the characteristic equation
of 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 the
characteristic equation of A.
The statement is true. It is the definition of the algebraic multiplicity of an
eigenvalue 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.

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