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Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) E (v1, v2) := (u1 + v1 + 3, u2 + v2 – 1) and scalar multiplication by a O (u1, u2) := (au1 + 3a – 3, au2 – a + 1). It can be shown that (V, H, D) is a vector space. Find the following: the sum: (2, –9) E (0, –8) =( the scalar multiple: -70 (2, –9) =( the zero vector: " 0 "=( the additive inverse "-v" of v = (x,y): » -v "=( ) (Must be in terms of x and y)

Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) E (v1, v2) := (u1 + v1 + 3, u2 + v2 – 1) and scalar multiplication by a O (u1, u2) := (au1 + 3a – 3, au2 – a + 1). It can be shown that (V, H, D) is a vector space. Find the following: the sum: (2, –9) E (0, –8) =( the scalar multiple: -70 (2, –9) =( the zero vector: " 0 "=( the additive inverse "-v" of v = (x,y): » -v "=( ) (Must be in terms of x and 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) (v1, v2) := and scalar multiplication by a O (u1, u2) := (au1 + 3a – 3, au2 – a + 1). It can be shown that (V, H, D) is a vector space. Find the following: (u1 + v1 + 3, u2 + v2 – 1) - the sum: (2, –9) H (0, –8) =( the scalar multiple: -70 (2, –9) =( the zero vector: " 0 "=( the additive inverse "-v" of v = (x, y): » -v "=( )( Must be in terms of x and y)
Transcribed Image Text:Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) (v1, v2) := and scalar multiplication by a O (u1, u2) := (au1 + 3a – 3, au2 – a + 1). It can be shown that (V, H, D) is a vector space. Find the following: (u1 + v1 + 3, u2 + v2 – 1) - the sum: (2, –9) H (0, –8) =( the scalar multiple: -70 (2, –9) =( the zero vector: " 0 "=( the additive inverse "-v" of v = (x, y): » -v "=( )( Must be in terms of x and y)
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