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Vector Subspaces

  1. Sep 4, 2012 #1
    Could someone please help me with the following question with a guided step by step answer:

    Show that T = (x, y, z) : -1 ≤ x + y + z ≤ 1
    is not a vector subspace of R3

    Thanks!
     
  2. jcsd
  3. Sep 4, 2012 #2

    $$(1,0,0)\in T\,\,\,but\,\,\,2(1,0,0)=(2,0,0)\notin T$$

    Thus T cannot be v. subspace as it isn't closed under scalar multiplication

    DonAntonio
     
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