Which of the following sets is not a vector subspace in the vector space R^3? (a) {(a, b, c) ER3 | 2a = 3c}.(b) {(a, b, c) ER3 | a = 0, b = 3c}.(c) {(a+b, ab, 2a + b) | a, b R}.(d) {(a, 2a, a) a € R}.(e) {(a, b, c) R³ |a-b+c=1}.

(a), (b) , (c), (d) are subspaces .

Answered: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a,…

(a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R} (d) {(a, 2a, a) a € R}. (e) {(a, b, c) R3 |a-b+c=1}.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 2E

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Question

Which of the following sets is not a vector subspace in the vector space R^3?

(a) {(a, b, c) ER3 | 2a = 3c}.
(b) {(a, b, c) ER3 | a = 0, b = 3c}.
(c) {(a+b, ab, 2a + b) | a, b R}.
(d) {(a, 2a, a) a € R}.
(e) {(a, b, c) R³ |a-b+c=1}.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution