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Let V = R. For u, v e V and a e R define vector addition by u H v := u + v – 1 and scalar multiplication by a O u := au - a + 1. It can be shown that (V, , 0) is a vector space. Find the following: the sum: 5 8 2 = the scalar multiple: 5 O 5 = the zero vector: " 0 "= the additive inverse " -v " of v = x: (Must be in terms of x)

Let V = R. For u, v e V and a e R define vector addition by u H v := u + v – 1 and scalar multiplication by a O u := au - a + 1. It can be shown that (V, , 0) is a vector space. Find the following: the sum: 5 8 2 = the scalar multiple: 5 O 5 = the zero vector: " 0 "= the additive inverse " -v " of v = x: (Must be in terms of x)

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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Let V = R. For u, v E V and a e R define vector addition by u H v := u + v – 1 and scalar multiplication by a Ou := au - a + 1. It can be shown that (V, H, 0) is a vector space. Find the following: %3D the sum: 5田2= the scalar multiple: 5 O 5 the zero vector: the additive inverse v " of v = x: ( Must be in terms of x)
Transcribed Image Text:Let V = R. For u, v E V and a e R define vector addition by u H v := u + v – 1 and scalar multiplication by a Ou := au - a + 1. It can be shown that (V, H, 0) is a vector space. Find the following: %3D the sum: 5田2= the scalar multiple: 5 O 5 the zero vector: the additive inverse v " of v = x: ( Must be in terms of x)
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