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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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