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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 + 1, u2 + v2 + 3) and scalar multiplication by a O (u1, u2) := (au, + a – 1, auz + 3a – 3). It can be shown that (V, H, O) is a vector space over the scalar field R. Find the following: the sum: (9, –1) H(-5, 7) =( the scalar multiple: 10 (9, –1) =( the zero vector: Oy =( the additive inverse of (x, y): B(x, y) =(

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 + 1, u2 + v2 + 3) and scalar multiplication by a O (u1, u2) := (au, + a – 1, auz + 3a – 3). It can be shown that (V, H, O) is a vector space over the scalar field R. Find the following: the sum: (9, –1) H(-5, 7) =( the scalar multiple: 10 (9, –1) =( the zero vector: Oy =( the additive inverse of (x, y): B(x, 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 = R?. For (u1, U2), (V1, V2) e V and a e R define vector addition by (u1, U2) H (v1, V2) := (u1 + vị + 1, u2 + v2 + 3) and scalar multiplication by a O (u1, u2) := (au, + a – 1, auz + 3a – 3). It can be shown that (V, H, O) is a vector space over the scalar field R. Find the following: the sum: (9, –1) H(-5, 7) =( the scalar multiple: 10 (9, –1) =( the zero vector: Oy =( the additive inverse of (x, y): B(2, 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 + 1, u2 + v2 + 3) and scalar multiplication by a O (u1, u2) := (au, + a – 1, auz + 3a – 3). It can be shown that (V, H, O) is a vector space over the scalar field R. Find the following: the sum: (9, –1) H(-5, 7) =( the scalar multiple: 10 (9, –1) =( the zero vector: Oy =( the additive inverse of (x, y): B(2, y) =(
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