Let V be the set {(x, y) | x, y ≤ R} with addition operation defined by (x1, Y₁) ⇒ (X2, Y2) = (x1 + x2, Y₁Y2) and scalar multiplication defined by a Ⓒ (x, y) = (x, 0). Show that V is not a vector space by determining which of the 10 vector space axioms are not true for V. Enter your answer as a comma separated list such as 3, 5, 6 if axioms numbered 3, 5 and 6 fail to be true.
Let V be the set {(x, y) | x, y ≤ R} with addition operation defined by (x1, Y₁) ⇒ (X2, Y2) = (x1 + x2, Y₁Y2) and scalar multiplication defined by a Ⓒ (x, y) = (x, 0). Show that V is not a vector space by determining which of the 10 vector space axioms are not true for V. Enter your answer as a comma separated list such as 3, 5, 6 if axioms numbered 3, 5 and 6 fail to be true.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 3ECP
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The question has two parts:
a) I have to find which of the axioms are not true for V.
b) Explain why each vector space axiom I chose in a) failed to be true.
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