Let V=R². For (u₁, U₂), (v₁, v₂) € V and a € R define vector addition by (u₁, ₂) (V₁, V₂) = (U₁ + v₁1, u2+ v2 - 3) and scalar multiplication by a □ (u₁, 1₂) := (au₁ —a +1, au₂ – 3a +3). It can be shown that (V,B, D) is a vector space over the scalar field R. Find the following: the sum: (-6, 0) (9,2)=( the scalar multiple: 40 (-6,0) =( the zero vector: Oy =( the additive inverse of (x, y): B(x, y) =(
Let V=R². For (u₁, U₂), (v₁, v₂) € V and a € R define vector addition by (u₁, ₂) (V₁, V₂) = (U₁ + v₁1, u2+ v2 - 3) and scalar multiplication by a □ (u₁, 1₂) := (au₁ —a +1, au₂ – 3a +3). It can be shown that (V,B, D) is a vector space over the scalar field R. Find the following: the sum: (-6, 0) (9,2)=( the scalar multiple: 40 (-6,0) =( the zero vector: Oy =( the additive inverse of (x, y): B(x, y) =(
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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Question
![Let V = R². For (u1, U2), (V1, V₂) ≤ V and a E R define vector addition by (u₁, U2) = (v₁, v₂) := (U₁ + V₁ − 1, U2 + v₂ − 3) and scalar multiplication
-
-
by a □ (u₁, U₂) := (au₁ — a + 1, au2 − 3a + 3). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following:
the sum:
(-6, 0) (9,2)=(
the scalar multiple:
40 (-6,0) =(
the zero vector:
0₁=(
the additive inverse of (x, y):
=(x, y) =(
"
1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2F1a58a351-3c4b-4218-bb31-085e4b0669ba%2Fvrj1lmc_processed.png&w=3840&q=75)
Transcribed Image Text:Let V = R². For (u1, U2), (V1, V₂) ≤ V and a E R define vector addition by (u₁, U2) = (v₁, v₂) := (U₁ + V₁ − 1, U2 + v₂ − 3) and scalar multiplication
-
-
by a □ (u₁, U₂) := (au₁ — a + 1, au2 − 3a + 3). It can be shown that (V, , ) is a vector space over the scalar field R. Find the following:
the sum:
(-6, 0) (9,2)=(
the scalar multiple:
40 (-6,0) =(
the zero vector:
0₁=(
the additive inverse of (x, y):
=(x, y) =(
"
1)
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