Let V = (3, 00). For u, v e V and a e R define vector addition by u H v := uv – 3(u + v) + 12 and scalar multiplication by (u – 3)a + 3. It can be shown that (V, H, O) is a vector space over the scalar field R. Find the following: a O u := the sum: 788 = the scalar multiple: -4 O 7 = the additive inverse of 7: 87 = the zero vector: Oy the additive inverse of x:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let V = (3, x). For u, v E V and a e R define vector addition by u H v := uv
3(u + v) + 12 and scalar multiplication by
-
a D u :=
(u – 3)ª + 3. It can be shown that (V, H, D) is a vector space over the scalar field R. Find the following:
the sum:
7田8
the scalar multiple:
-4 O 7 =
the additive inverse of 7:
日7 =
the zero vector:
Oy
the additive inverse of x:
Transcribed Image Text:Let V = (3, x). For u, v E V and a e R define vector addition by u H v := uv 3(u + v) + 12 and scalar multiplication by - a D u := (u – 3)ª + 3. It can be shown that (V, H, D) is a vector space over the scalar field R. Find the following: the sum: 7田8 the scalar multiple: -4 O 7 = the additive inverse of 7: 日7 = the zero vector: Oy the additive inverse of x:
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