Let V = R². For (u₁, U2), (v1, v2₂) € V and a € R define vector addition by (U1, U2) = (v1, v2) := (u₁ + v₁ + 2, u2+ v2 − 2) and scalar multiplication by a □ (µ₁, U2) := (au₁ + 2a − 2, au₂ − 2a + 2). It can be shown that (V,, ) is a vector space over the scalar field R. Find the following: the sum: (6, −5) = (–9, 3) = the scalar multiple: − 8 □ (6, −5) =) the zero vector: the additive inverse of (x, y): =(x, y) =00)
Let V = R². For (u₁, U2), (v1, v2₂) € V and a € R define vector addition by (U1, U2) = (v1, v2) := (u₁ + v₁ + 2, u2+ v2 − 2) and scalar multiplication by a □ (µ₁, U2) := (au₁ + 2a − 2, au₂ − 2a + 2). It can be shown that (V,, ) is a vector space over the scalar field R. Find the following: the sum: (6, −5) = (–9, 3) = the scalar multiple: − 8 □ (6, −5) =) the zero vector: the additive inverse of (x, y): =(x, y) =00)
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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Transcribed Image Text:Let V = R². For (u₁, U2), (v₁, v2) € V and a € R define vector addition by
(U₁, U₂) (V₁, V₂) :
== (u₁ + v₁+2, u₂+2 − 2) and scalar multiplication by
a□ (U₁, U₂) = (au₁ + 2a − 2, auz - 2a + 2). It can be shown that (V,B, ) is a vector space
over the scalar field R. Find the following:
the sum:
(6,-5) (-9,3)
the scalar multiple:
-8 (6,-5) =
the zero vector:
=
Ov
the additive inverse of (x, y):
B(x, y) =
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