In the following list of subsets of R3 , select the ones that are subspaces of R3...

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In the following list of subsets of R³ ,select the ones that are subspaces ofR³ (multiple answers).
(As usual, incorrect answers will earn you negative points)
Entire R³
{ (x+y, x-y, y ) | x,y are real numbers }
{ (x,y,z) | x,y,z are all nonnegative real numbers }
{ ( x, -x, 2x ) | x is a real number }
{ (1,1,1) }
{ (x,y,3) | x,y are real numbers }
{ (0,0,0) }
{ (x+1, y+1, z+1) | x,y,z are real numbers }
{ (x,y,0) | x,y are real numbers }
{ (x,y,z) | x + y + z = 1 }

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4.1 Ratings (740 Votes)

Entire R3 is a subspace of R3 as every vector space is a subspace of itself V xy xy y xy are real numbers is a subspace of R3 as V R3 is closed under vector addition and scalar multiplication and also contains the zero vector V xyz xyz are all nonnegative real numbers is not a See Answer

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		Entire R³
		{ (x+y, x-y, y ) \| x,y are real numbers }
		{ (x,y,z) \| x,y,z are all nonnegative real numbers }
		{ ( x, -x, 2x ) \| x is a real number }
		{ (1,1,1) }
		{ (x,y,3) \| x,y are real numbers }
		{ (0,0,0) }
		{ (x+1, y+1, z+1) \| x,y,z are real numbers }
		{ (x,y,0) \| x,y are real numbers }
		{ (x,y,z) \| x + y + z = 1 }