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Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ + V₁ + 3, U₂ + V₂ — 1) and scalar multiplication by a(u₁,₂)=(au, +3a-3, au₂-a-1). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following: the sum: (4, 5) E (3, −8) − E( the scalar multiple: -50 (4,5) ( the zero vector: Oy the additive inverse of (z,y) B(z,y)=(

Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ + V₁ + 3, U₂ + V₂ — 1) and scalar multiplication by a(u₁,₂)=(au, +3a-3, au₂-a-1). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following: the sum: (4, 5) E (3, −8) − E( the scalar multiple: -50 (4,5) ( the zero vector: Oy the additive inverse of (z,y) B(z,y)=(

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=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ + V₁ + 3, U₂ + V₂ — 1) and scalar multiplication by a(u₁,₂)=(au₁ +3a-3, au₂-a-1). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following. the sum: (4, 5) H (3, −8) − E( the scalar multiple -50 (4,5) ( the zero vector: Oy the additive inverse of (z,y) B(z,y)=(
Transcribed Image Text:Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ + V₁ + 3, U₂ + V₂ — 1) and scalar multiplication by a(u₁,₂)=(au₁ +3a-3, au₂-a-1). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following. the sum: (4, 5) H (3, −8) − E( the scalar multiple -50 (4,5) ( the zero vector: Oy the additive inverse of (z,y) B(z,y)=(
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