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Let V = R². For (u₁, U2), (v₁, v₂) € V and a ER define vector addition by (u₁, U₂) (V1₁, V₂) = = (U₁ + V₁ − 1, U₂ + V2 − 3) and scalar multiplication by a (u₁, ₂) = (au₁ — a +1, au2 − 3a + 3). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following: the sum: (-6, 0) (9,2)=(2 the scalar multiple: 40 (-6,0) =( the zero vector: Ov 1 the additive inverse of (x, y): B(x, y) =( 3 -1

Let V = R². For (u₁, U2), (v₁, v₂) € V and a ER define vector addition by (u₁, U₂) (V1₁, V₂) = = (U₁ + V₁ − 1, U₂ + V2 − 3) and scalar multiplication by a (u₁, ₂) = (au₁ — a +1, au2 − 3a + 3). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following: the sum: (-6, 0) (9,2)=(2 the scalar multiple: 40 (-6,0) =( the zero vector: Ov 1 the additive inverse of (x, y): B(x, y) =( 3 -1

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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: (U₁ + v₁ 1, U2 + V₂ 3) and scalar multiplication Let V = R². For (u1, U2), (V1, V₂) ≤ V and a € R define vector addition by (u₁1, U2) = (V1, V₂) := (au₁ — a + 1, au2 − 3a + 3). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following: by a □ (u₁, U₂) : the sum: := (−6, 0) = (9, 2) =( 2 the scalar multiple: 40 (-6,0) =( the zero vector: 0₁ (1 the additive inverse of (x, y): B(x, y) =( " 3 " T 7
Transcribed Image Text:: (U₁ + v₁ 1, U2 + V₂ 3) and scalar multiplication Let V = R². For (u1, U2), (V1, V₂) ≤ V and a € R define vector addition by (u₁1, U2) = (V1, V₂) := (au₁ — a + 1, au2 − 3a + 3). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following: by a □ (u₁, U₂) : the sum: := (−6, 0) = (9, 2) =( 2 the scalar multiple: 40 (-6,0) =( the zero vector: 0₁ (1 the additive inverse of (x, y): B(x, y) =( " 3 " T 7
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