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. Choose the correct answer below. O 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. O B. The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A. O c. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A. O D. The 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.

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. Choose the correct answer below. O 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. O B. The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A. O c. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A. O D. The 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.

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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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.
Choose the correct answer below.
O 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.
B. The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A.
C. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A.
O D. The statement is false. The multiplicity of a root r of the characteristic equation of A is called the geometric multiplicity of r as an eigenvalue of
A.
O O O O

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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.