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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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masterpiece11 | Student | (Level 1) Salutatorian

Posted March 20, 2013 at 10:59 PM 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.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 23, 2013 at 11:21 AM (Answer #1)

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Ans B .W is not a vector space because it is not closed under scalar multiplication.

let u=(1,1,1)

-5u=(-5,-5,-5) is not in W.

 

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