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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) := (u1+ v1 + 3, 2 + v2 – 1) and scalar multiplication by a O (u1, u2) := (au1+ 3a – 3, au2 – a + 1). It can be shown that (V,H,0) is a vector space. Find the following: the sum: (2, —9) в (0, —8) %3D( 5 -18 the scalar multiple: -70 (2, –9) =( -38 57 the zero vector: " 0 "=( -1 3 the additive inverse "–v" of v (x, y): "=( 3 -1 ) (Must be in terms of x and y) -v

Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) # (v1, v2) := (u1+ v1 + 3, 2 + v2 – 1) and scalar multiplication by a O (u1, u2) := (au1+ 3a – 3, au2 – a + 1). It can be shown that (V,H,0) is a vector space. Find the following: the sum: (2, —9) в (0, —8) %3D( 5 -18 the scalar multiple: -70 (2, –9) =( -38 57 the zero vector: " 0 "=( -1 3 the additive inverse "–v" of v (x, y): "=( 3 -1 ) (Must be in terms of x and y) -v

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) := (u1+ v1 + 3, u2 + v2 a O (u1, u2) - 1) and scalar multiplication by := (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) в (0, —8) %3D( 5 -18 the scalar multiple: -70 (2, –9) =( -38 57 the zero vector: " 0 "=( -1 22 3 the additive inverse "-v" of v = (x,y): " -v "=( 3 )(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) := (u1+ v1 + 3, u2 + v2 a O (u1, u2) - 1) and scalar multiplication by := (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) в (0, —8) %3D( 5 -18 the scalar multiple: -70 (2, –9) =( -38 57 the zero vector: " 0 "=( -1 22 3 the additive inverse "-v" of v = (x,y): " -v "=( 3 )(Must be in terms of x and y)
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