Problem 2: If V=R^3 is a vector space and let H be a subset of V and is defined as H=\{

Holly Guerrero

Holly Guerrero

Answered question

2022-01-04

Problem 2:
If V=R3 is a vector space and let H be a subset of V and is defined as H={(a,b,c):c2+b2=0,a0}. Show that H is not subspace of vector space
Problem 3
Let V=R3 be a vector space and let W be a subset of V, where W={(a,b,c):a2=b2}. Determine whether W is a subspace of vector space or not.

Answer & Explanation

braodagxj

braodagxj

Beginner2022-01-05Added 38 answers

Problem 2:
V=R3
H={(a,b,c):c2+b2=0,a0}
At x=(1,0,0)H
But α=2 is scalar in R
αx=(2)(1,0,0)
=(2,0,0)H(2<0)
Not subspace of vector space V
Piosellisf

Piosellisf

Beginner2022-01-06Added 40 answers

Problem 3:
V=R3
W={(a,b,c):a2=b2}
At x(1,1,0)H
At y(1,1,0)H
But x+y=(2,0,0)H
2202
Not subspace of vector space V

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