Vector Spaces & Subspaces, Linear Algebra

  • Thread starter kash25
  • Start date
  • #1
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Homework Statement



Let V be a vector space and U a subspace of V . For a given x ∈ V , define T=
{x + u | u ∈ U }. Show that T is a subspace of V if and only if x ∈ U .


Homework Equations


Subspace Test:
1: The 0 vector of V is included in T.
2: T is closed under vector addition
3: T is closed under scalar multiplication


The Attempt at a Solution


I do not know how to show this...
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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You're not trying very hard. Start with the forward direction. Show T is a subspace if x is in U. Try showing in this case T=U.
 

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