Which of the following statements are always true?(i) If A is a 3 x 3 diagonalizable matrix then A has 3 distinct eigenvalues.(ii) If the characteristic polynomial of a matrix A is equal to (2 – 3)*(2– 6)°(2 – 7)š then the eigenvalue 2 = 3has a geometric multiplicity of 4.(iii) If A is similar to B, and B is symmetric, then A' is similar to B.A) (i) and (ii) only (B) (ii) and (iii) only (C) (ii) only (D) none of them (E) (iii) only (F) (i) onlyG) all of them (H) (i) and (iii) only

Which of the following statements are always true? (i) If A is a 3 × 3 diagonalizable matrix then A has 3 distinct eigenvalues. (ii) If the characteristic polynomial of a matrix A is equal to (1 – 3)*(2 – 6)°(2 – 7)8 then the eigenvalue 2 has a geometric multiplicity of 4. (iii) If A is similar to B, and B is symmetric, then A' is similar to B. = 3 A) (i) and (ii) only (B) (ii) and (iii) only (C) (ii) only (D) none of them (E) (iii) only (F) (i) only G) all of them (H) (i) and (iii) only

Which of the following statements are always true? (i) If A is a 3 × 3 diagonalizable matrix then A has 3 distinct eigenvalues. (ii) If the characteristic polynomial of a matrix A is equal to (1 – 3)*(2 – 6)°(2 – 7)8 then the eigenvalue 2 has a geometric multiplicity of 4. (iii) If A is similar to B, and B is symmetric, then A' is similar to B. = 3 A) (i) and (ii) only (B) (ii) and (iii) only (C) (ii) only (D) none of them (E) (iii) only (F) (i) only G) all of them (H) (i) and (iii) only

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...

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