Which of the following sets are closed under addition? (i) The set of all vectors in R² of the form (a, b) where b = a. (ii) The set of all 3 × 3 matrices that have the vector [2 2 1] as an eigenvector. (iii) The set of all polynomials in P₂ of the form ao + -a₁x + a₂x² where ao = az A) none of them (B) (i) and (ii) only (C) (ii) and (iii) only (D) all of them (E) (i) and (iii) only (F) (iii) only G) (i) only (H) (ii) only
Which of the following sets are closed under addition? (i) The set of all vectors in R² of the form (a, b) where b = a. (ii) The set of all 3 × 3 matrices that have the vector [2 2 1] as an eigenvector. (iii) The set of all polynomials in P₂ of the form ao + -a₁x + a₂x² where ao = az A) none of them (B) (i) and (ii) only (C) (ii) and (iii) only (D) all of them (E) (i) and (iii) only (F) (iii) only G) (i) only (H) (ii) only
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Which of the following sets are closed under addition?
(i) The set of all vectors in R² of the form (a, b) where b = a.
(ii) The set of all 3 × 3 matrices that have the vector [221] as an eigenvector.
(iii) The set of all polynomials in P2 of the form að + a₁ x + a2 x² where a = az.
A) none of them (B) (i) and (ii) only (C) (ii) and (iii) only (D) all of them (E) (i) and (iii) only (F) (iii) only
G) (i) only (H) (ii) only](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2F0d421e41-4c6f-4c2f-8cbf-5ffe144fecb2%2F353qyio_processed.png&w=3840&q=75)
Transcribed Image Text:Which of the following sets are closed under addition?
(i) The set of all vectors in R² of the form (a, b) where b = a.
(ii) The set of all 3 × 3 matrices that have the vector [221] as an eigenvector.
(iii) The set of all polynomials in P2 of the form að + a₁ x + a2 x² where a = az.
A) none of them (B) (i) and (ii) only (C) (ii) and (iii) only (D) all of them (E) (i) and (iii) only (F) (iii) only
G) (i) only (H) (ii) only
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