SOLUTION: Question; Determine whether or not W is a subspace of R3, with justification (general proof). W={(x,y,x+y); x and y are real)}. I have a trouble in proving(in general, not specifi

Question 39593: Question; Determine whether or not W is a subspace of R3, with justification (general proof).
W={(x,y,x+y); x and y are real)}. I have a trouble in proving(in general, not specific numbers) the closure axioms(addition and scalar multiplication). Please help!
Answer by cininnatus(12) (Show Source): You can put this solution on YOUR website!
You need to show that if W contains (x,y,x+y) then it must also contain (x+u1,y+c*u2,u1+c*u2). Where c is a scalar and u1,u2 are real numbers. This follows directly from the fact that addition and multiplication (+,*) with real numbers is closed, so if y,c,u2 are all real numbers then so must y+c*u2 be a real number; etc.

You also need to show that W is not empty, just take x=y=0 and observe that the zero vector is in W.
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