Let V = R². For (₁, U₂), (V₁, V₂) € V and a ER define vector addition by (4₁, U₂) (V₁, V₂) := (U₁ + V₂ + 3, U₂ +2 +2) and scalar multiplication by a (u₁, ₂) = (au₁ +3a-3, au₂ + 2a-2). It can shown that (V, BB, ) is a vector space over the scalar field R. Find the following: the sum (-9,6) (9,9)=( the scalar multiple: 90 (-9,6)=( the zero vector: Oy =( the additive inverse of (x, y): B(x,y)=(

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let V = R?. For (u1, u2), (v1, v2) E V and a e R define vector addition by (u1, U2) H (v1, v2) := (u1 + vị + 3, uz + v2 + 2) and scalar multiplication by a O (u1, uz) := (au, + 3a – 3, auz + 2a – 2). It can be
shown that (V, B,O) is a vector space over the scalar field R. Find the following:
the sum
(-9, 6) H (9,9) =(
the scalar multiple:
90(-9,6) =(
the zero vector:
Oy =
the additive inverse of (z, y):
E(1, y) =
Transcribed Image Text:Let V = R?. For (u1, u2), (v1, v2) E V and a e R define vector addition by (u1, U2) H (v1, v2) := (u1 + vị + 3, uz + v2 + 2) and scalar multiplication by a O (u1, uz) := (au, + 3a – 3, auz + 2a – 2). It can be shown that (V, B,O) is a vector space over the scalar field R. Find the following: the sum (-9, 6) H (9,9) =( the scalar multiple: 90(-9,6) =( the zero vector: Oy = the additive inverse of (z, y): E(1, y) =
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