Let V R. For u, v E V and a ER = - define vector addition by uv := u + v − 3 and scalar multiplication by au := au 3a + 3. It can be shown that (V, E, O) is a vector space over the scalar field R. Find the following: the sum: -8-4 = = the scalar multiple: -5-8 = the zero vector: Ov - = 8x the additive inverse of x: =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let V = R. For u, v E V and a E R
define vector addition by uv := u + v − 3
and scalar multiplication by
au: au
3a + 3. It can be shown that
(V, B, O) is a vector space over the scalar field
R. Find the following:
the sum:
-8-4 =
the scalar multiple:
-5-8: =
the zero vector:
Ov
-
=
the additive inverse of x:
8x =
Transcribed Image Text:Let V = R. For u, v E V and a E R define vector addition by uv := u + v − 3 and scalar multiplication by au: au 3a + 3. It can be shown that (V, B, O) is a vector space over the scalar field R. Find the following: the sum: -8-4 = the scalar multiple: -5-8: = the zero vector: Ov - = the additive inverse of x: 8x =
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