Q1. Let u= (1, 1), addition and scalar multiplication on Vas; u+v=(₁+y₁-1, 2+2-1) and a.u = (ay, 2₁). (i). Compute, u + vand k.u, if u = (-1,3), (2,0) and k = 5. (ii). Show that V is not a vector space with given addition and scalar mul- tiplication. (2.92) EV = R² and k € R. Then we define
Q1. Let u= (1, 1), addition and scalar multiplication on Vas; u+v=(₁+y₁-1, 2+2-1) and a.u = (ay, 2₁). (i). Compute, u + vand k.u, if u = (-1,3), (2,0) and k = 5. (ii). Show that V is not a vector space with given addition and scalar mul- tiplication. (2.92) EV = R² and k € R. Then we define
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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![Q1. Let u (₁,1), v= (2, 2) V=R² and ke R. Then we define
addition and scalar multiplication on Vas;
u+v= (₁+y₁-1, 2+92-1) and a.u = (ay₁, 2₁).
(i). Compute, u+v and k.u, if u = (-1,3), v= (2,0) and k = 5.
(ii). Show that V is not a vector space with given addition and scalar mul-
tiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dbb4e54-f41e-4a5c-8a16-0f1fa137640d%2F1fc85489-95b7-486b-b505-ef50a8a1b8dd%2Fw0ngsnb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1. Let u (₁,1), v= (2, 2) V=R² and ke R. Then we define
addition and scalar multiplication on Vas;
u+v= (₁+y₁-1, 2+92-1) and a.u = (ay₁, 2₁).
(i). Compute, u+v and k.u, if u = (-1,3), v= (2,0) and k = 5.
(ii). Show that V is not a vector space with given addition and scalar mul-
tiplication.
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