Show the set S is a subspace of Real Numbers^3

  • Thread starter racshot65
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  • #1
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Homework Statement



Show that set S = {(x , y, z ) | x + 2y − z = 0} is a subspace of Real Numbers^3.


Homework Equations



A subspace needs to be closed under addition and scalar multiplication

The Attempt at a Solution



S = { (x, y, x+2y) | x, y are elements of Real Numbers }

Now where do I go from here what do I have to do to show closure under addition and scalar multiplication ?


Thanks !
 

Answers and Replies

  • #2
LCKurtz
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Just use the definitions:

Show that if you have two elements in S that their sum is in S.

Show if you have an element in S that a constant times it is in S.
 

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