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Determine whether the following sets with the corresponding vector addi- tion and scalar multiplication form vector spaces. a) Let V = {(a₁, a2): a1, a2 € R}. For (a₁, a2), (b₁,b₂) EV and c € R, define: (a1, a2)+(b₁,b₂) = (a₁ +2b1, a2 +3b2) and c(a1, a2) = (ca₁,ca2)

Determine whether the following sets with the corresponding vector addi- tion and scalar multiplication form vector spaces. a) Let V = {(a₁, a2): a1, a2 € R}. For (a₁, a2), (b₁,b₂) EV and c € R, define: (a1, a2)+(b₁,b₂) = (a₁ +2b1, a2 +3b2) and c(a1, a2) = (ca₁,ca2)

Advanced Engineering Mathematics
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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2. Determine whether the following sets with the corresponding vector addi- tion and scalar multiplication form vector spaces. a) Let V = {(a₁, a2): a1, a2 € R}. For (a₁, a2), (b₁,b₂) € V and c € R, define: (a₁, a2)+(b₁,b2) = (a₁ +2b₁, a2 + 3b2) and c(a₁, a2) = (ca₁,ca2) b) Let V = {(a1, a2): a1, a2 € R}. For (a1, a2) € V and c € R, define: c(a1, a2) = (ca₁,0)
Transcribed Image Text:2. Determine whether the following sets with the corresponding vector addi- tion and scalar multiplication form vector spaces. a) Let V = {(a₁, a2): a1, a2 € R}. For (a₁, a2), (b₁,b₂) € V and c € R, define: (a₁, a2)+(b₁,b2) = (a₁ +2b₁, a2 + 3b2) and c(a₁, a2) = (ca₁,ca2) b) Let V = {(a1, a2): a1, a2 € R}. For (a1, a2) € V and c € R, define: c(a1, a2) = (ca₁,0)
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