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Let W be the set of all vectors [[a],[b],[c]] such that a + b + c > 2. Determine if...

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gomezzzzzzzzz... | Student | eNoter

Posted March 26, 2013 at 2:17 AM via web

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Let W be the set of all vectors [[a],[b],[c]]

such that a + b + c > 2.


Determine if W is a subspace of R^3 and check all correct answers below.

A. W is a not vector space because it is not closed under the addition.
B. W is not a vector space because it is not closed under scalar multiplication.
C. W is not a vector space because it does not have a zero element.
D. W is a vector space because it is the solution set of a homogeneous linear system.

The previous answers to this question have all been incorrect.

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pramodpandey | College Teacher | Valedictorian

Posted March 26, 2013 at 8:49 AM (Answer #1)

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1.W is not a vector space because it is not closed under scalar multiplication.
2. W is not a vector space because it does not have a zero element.

u and v are in W such that

u(1,1,1) and v(0,2,0)

u+v in W

-1 u is not in W  ( Not closed under scalar multiplication)

x(0,0,0) is vector

x is not in W.

because  0+0+0 not > 0

 

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