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Pose that À = 6 is an eigenvalue of a matrix A. Then the equation Ax = 6x has exa pose that the characteristic polynomial of a matrix A is 1(1 – 7)*(1 – 6). Then the ery 300 × 300 upper triangular matrix has 300 distinct eigenvalues. (B) (i) only (C) none of them (D) (1) and (ii) only (E) (ii) only (F) (ii) and ( i1) only (H) all of them

Pose that À = 6 is an eigenvalue of a matrix A. Then the equation Ax = 6x has exa pose that the characteristic polynomial of a matrix A is 1(1 – 7)*(1 – 6). Then the ery 300 × 300 upper triangular matrix has 300 distinct eigenvalues. (B) (i) only (C) none of them (D) (1) and (ii) only (E) (ii) only (F) (ii) and ( i1) only (H) all of them

Algebra and Trigonometry (6th Edition)
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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Problem #19: Which of the following statements are always true? (1) Suppose that 1 = 6 is an eigenvalue of a matrix A. Then the equation Ax = 6x has exactly one solution. (i11) Suppose that the characteristic polynomial of a matrix A is 1(1 - 7)*a – 6)'. Then the determinant of A is nonzero. (iii) Every 300 × 300 upper triangular matrix has 300 distinct eigenvalues. (A) (iii) only (B) (i) only (C) none of them (D) (i) and (ii) only (E) (ii) only (F) (ii) and (ii1) only (G) (i) and (iii) only (H) all of them
Transcribed Image Text:Problem #19: Which of the following statements are always true? (1) Suppose that 1 = 6 is an eigenvalue of a matrix A. Then the equation Ax = 6x has exactly one solution. (i11) Suppose that the characteristic polynomial of a matrix A is 1(1 - 7)*a – 6)'. Then the determinant of A is nonzero. (iii) Every 300 × 300 upper triangular matrix has 300 distinct eigenvalues. (A) (iii) only (B) (i) only (C) none of them (D) (i) and (ii) only (E) (ii) only (F) (ii) and (ii1) only (G) (i) and (iii) only (H) all of them
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