(1) True or False? Justify your answer. (a) There exists a matrix A with eigenvalue 4 whose algebraic multiplicity is 1 and geo- metric multiplicity is 3. Justification: (b) Matrix 3 4 Justification: True Justification: in Z5 is digonalizable. True False (c) Two matrices A and B are similar if they have the same list of eigenvalues that have the same algebraic multiplicity. True False False

(1) True or False? Justify your answer. (a) There exists a matrix A with eigenvalue 4 whose algebraic multiplicity is 1 and geo- metric multiplicity is 3. Justification: (b) Matrix 3 4 Justification: True Justification: in Z5 is digonalizable. True False (c) Two matrices A and B are similar if they have the same list of eigenvalues that have the same algebraic multiplicity. True False False

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

(1)
True or False? Justify your answer.
(a) There exists a matrix A with eigenvalue 4 whose algebraic multiplicity is 1 and geo-
metric multiplicity is 3.
Justification:
(b) Matrix
[13]
Justification:
True
in Z5 is digonalizable.
True
Justification:
(c) Two matrices A and B are similar if they have the same list of eigenvalues that have
the same algebraic multiplicity.
False
Justification:
True
False
False
(d) A square matrix with the characteristic polynomial A5 - 314-2A³ +5A² - 4x + 2 is
invertible.
True
False
(e) If A and B are similar then both of them are diagonalizable.
True
False
Justification:

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