Suppose that A is a square matrix with characteristic polynomial (2-3)*(x-4)³ (2+1). (a) What are the dimensions of A? (Give n such that the dimensions are n x n.) (b) What are the eigenvalues of A? (Enter your answers as a comma-separated list.) λ = (c) Is A invertible? Yes No (d) What is the largest possible dimension for an eigenspace of A?

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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Suppose that A is a square matrix with characteristic polynomial (2-3)*(2-4)³ (2+1).
(a) What are the dimensions of A? (Give n such that the dimensions are n x n.)
n=
(b) What are the eigenvalues of A? (Enter your answers as a comma-separated list.)
λ =
(c) Is A invertible?
Yes
O No
(d) What is the largest possible dimension for an eigenspace of A?
Transcribed Image Text:Suppose that A is a square matrix with characteristic polynomial (2-3)*(2-4)³ (2+1). (a) What are the dimensions of A? (Give n such that the dimensions are n x n.) n= (b) What are the eigenvalues of A? (Enter your answers as a comma-separated list.) λ = (c) Is A invertible? Yes O No (d) What is the largest possible dimension for an eigenspace of A?
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