Which of the following sets are closed under scalar multiplication? (i) The set of all vectors in R² of the form (a, b) where a -5b=0. (ii) The set of all 2 × 2 matrices whose trace is equal to 2. (iii) The set of all polynomials in P₂ of the form að + a₁ x + a₂ x² where the product ao a₁ a2 ≤ 0. A) (i) only (B) (i) and (iii) only (C) all of them (D) (ii) only (E) (ii) and (iii) only (F) (i) and (ii) only G) (iii) only (H) none of them
Which of the following sets are closed under scalar multiplication? (i) The set of all vectors in R² of the form (a, b) where a -5b=0. (ii) The set of all 2 × 2 matrices whose trace is equal to 2. (iii) The set of all polynomials in P₂ of the form að + a₁ x + a₂ x² where the product ao a₁ a2 ≤ 0. A) (i) only (B) (i) and (iii) only (C) all of them (D) (ii) only (E) (ii) and (iii) only (F) (i) and (ii) only G) (iii) only (H) none of them
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 35E
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![Which of the following sets are closed under scalar multiplication?
(i) The set of all vectors in R² of the form (a, b) where a - 56 = 0.
(ii) The set of all 2 × 2 matrices whose trace is equal to 2.
(iii) The set of all polynomials in P2 of the form aŋ + a₁ x + a₂ x² where the product ao ª₁ a2 ≤ 0.
92
A) (i) only (B) (i) and (iii) only (C) all of them (D) (ii) only (E) (ii) and (iii) only (F) (i) and (ii) only
G) (iii) only (H) none of them](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2Fbfb83ced-82ad-47c9-9e67-aaffbcd6f9a5%2Fbe6qen7_processed.png&w=3840&q=75)
Transcribed Image Text:Which of the following sets are closed under scalar multiplication?
(i) The set of all vectors in R² of the form (a, b) where a - 56 = 0.
(ii) The set of all 2 × 2 matrices whose trace is equal to 2.
(iii) The set of all polynomials in P2 of the form aŋ + a₁ x + a₂ x² where the product ao ª₁ a2 ≤ 0.
92
A) (i) only (B) (i) and (iii) only (C) all of them (D) (ii) only (E) (ii) and (iii) only (F) (i) and (ii) only
G) (iii) only (H) none of them
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