Expert Answer to "Problem 2: If V=R3 is a vector space..."

Holly Guerrero

Answered question

2022-01-04

Problem 2:
If

V = R^{3}

is a vector space and let H be a subset of V and is defined as

H = {(a, b, c) : c^{2} + b^{2} = 0, a \geq 0}

. Show that H is not subspace of vector space
Problem 3
Let

V = R^{3}

be a vector space and let W be a subset of V, where

W = {(a, b, c) : a^{2} = b^{2}}

. Determine whether W is a subspace of vector space or not.

braodagxj

Beginner2022-01-05Added 38 answers

Problem 2:

V = R^{3}

H = {(a, b, c) : c^{2} + b^{2} = 0, a \geq 0}

x = (1, 0, 0) \in H

But

α = - 2

is scalar in R

α x = (- 2) (1, 0, 0)

= (- 2, 0, 0) \notin H (- 2 < 0)

Not subspace of vector space V

Piosellisf

Beginner2022-01-06Added 40 answers

Problem 3:

V = R^{3}

W = {(a, b, c) : a^{2} = b^{2}}

x (1, - 1, 0) \in H

y (1, 1, 0) \in H

But

x + y = (2, 0, 0) \notin H

∴ 2^{2} \neq 0^{2}

Not subspace of vector space V

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