Solving: Vector Subspaces Question in R3

[markovchain]

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!

 

[DonAntonio]

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