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(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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 48E: CAPSTONE Explain how to determine whether an nn matrix A is diagonalizable using a similar matrices,...
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(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:
Transcribed Image Text:(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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