Let V = R2. For (vị , v2), (W1, w2) E V and k ER define vector addition by: (vi, v2) O (W1, w2) := (v +w - 5, v2 + w2) and scalar multiplication by : ko (vi,v2) := (kv - 5k + 5, kvz). It can be shown that (V, . D) is a real vector space (all 10 axioms are true). Computer the following: the sum: (3, 3) (3,-4) =( the scalar multiple: -5 0 (3, 3) =( the zero vector: Oy =( the additive inverse of (x, y): e(x, y) =(
Let V = R2. For (vị , v2), (W1, w2) E V and k ER define vector addition by: (vi, v2) O (W1, w2) := (v +w - 5, v2 + w2) and scalar multiplication by : ko (vi,v2) := (kv - 5k + 5, kvz). It can be shown that (V, . D) is a real vector space (all 10 axioms are true). Computer the following: the sum: (3, 3) (3,-4) =( the scalar multiple: -5 0 (3, 3) =( the zero vector: Oy =( the additive inverse of (x, y): e(x, y) =(
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 44E
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Transcribed Image Text:Let V = R2. For (vị , v2), (W1, w2) E V and k ER define vector addition by :
(vi, v2) O (w1, w2) := (v + w-5, v2 + w2)
and scalar multiplication by :
ko (vi, v2) := (kvi - 5k + 5, kvz).
It can be shown that (V, B. O) is a real vector space (all 10 axioms are true).
Computer the following:
the sum:
(3, 3) (3,-4) =(
the scalar multiple:
-5 0 (3, 3) =(
the zero vector:
Oy =(
the additive inverse of (x, y):
e(x, y) =
Verify that the following Axioms are true:
• Axiom 4.
• Axiom 5.
• Axiom 7.
* For these three axioms, you must submit the complete solutions in MOODLE. *
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