(1.4) :(::)-(::) 3 4 3 4 %3D 2 2 2 2 Therefore Axiom 10 holds. Is this true or false? Give reasons for your answer. (1.5) V is not a vector space. Apart from the Axiom in [1.4], give 2 Axioms that do not hold. Explain clearly by giving examples.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 9E
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Question 1
Let V = M2 with addition and scalar multiplication defined as follows:
(::)-(; 1)-( n-3)
a +e +1 b+f +2
c+g –1 d+h – 3
and
a b
aa ab
с d
2
Transcribed Image Text:Question 1 Let V = M2 with addition and scalar multiplication defined as follows: (::)-(; 1)-( n-3) a +e +1 b+f +2 c+g –1 d+h – 3 and a b aa ab с d 2
(1.4)
(:)-(:)
3 4
1
2
3 4
%3D
2 2
Therefore Axiom 10 holds. Is this true or false? Give reasons for your answer.
(1.5) V is not a vector space. Apart from the Axiom in [1.4], give 2 Axioms that do not hold.
Explain clearly by giving examples.
Transcribed Image Text:(1.4) (:)-(:) 3 4 1 2 3 4 %3D 2 2 Therefore Axiom 10 holds. Is this true or false? Give reasons for your answer. (1.5) V is not a vector space. Apart from the Axiom in [1.4], give 2 Axioms that do not hold. Explain clearly by giving examples.
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