(1) If A is diagonalizable then cA is diagonalizable for any constant c. (i1) If the characteristic polynomial of a matrix A is equal to (1 - 5) (1– 7)°(1 – 8)* then the eigenvalue A = 5 has a geometric multiplicity of 9. (ii1) If A is similar to B, then A is similar to B.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Which of the following statements are always true?
(1) If A is diagonalizable then cA is diagonalizable for any constant c.
(i1) If the characteristic polynomial of a matrix A is equal to (1- 5) (1 – 7)°(a – 8)* then the eigenvalue 1
has a geometric multiplicity of 9.
(111) If A is similar to B, then A is similar to B.
= 5
(A) (1) and (iii) only (B) all of them (C) (i) only (D) (iii) only (E) (ii) and (iii) only (F) none of them
(G) (11) only (H) (1) and (ii) only
Transcribed Image Text:Which of the following statements are always true? (1) If A is diagonalizable then cA is diagonalizable for any constant c. (i1) If the characteristic polynomial of a matrix A is equal to (1- 5) (1 – 7)°(a – 8)* then the eigenvalue 1 has a geometric multiplicity of 9. (111) If A is similar to B, then A is similar to B. = 5 (A) (1) and (iii) only (B) all of them (C) (i) only (D) (iii) only (E) (ii) and (iii) only (F) none of them (G) (11) only (H) (1) and (ii) only
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