Vector Subspaces

  • #1
markovchain
1
0
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!
 

Answers and Replies

  • #2
DonAntonio
606
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!


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

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

DonAntonio
 

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