Problem 2: If V=R3 is a vector space and let H be a subset of...

Holly Guerrero

Holly Guerrero

Answered

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

Expert

2022-01-05Added 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

Expert

2022-01-06Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?