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

[racshot65]

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 !

 

[LCKurtz]

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.