1. The problem statement, all variables and given/known data Show that the system S is not a vector space by showing one of the axioms is not satisfied with the usual rules for addition and multiplication by a scalar in ℝ^{3} S={x(ℝ^{3}):2x_{1}+3x_{32}-4x_{23}=0} 2. Relevant equations 3. The attempt at a solution The subscripts for the x's are strange I think but I guess that shouldn't make a difference. But I'm really stuck on this I think it should be fairly easy though. but for example if I try closure under scalar multiplication or closure under addition I keep coming to a dead end because I don't know the value of the x's. ie λ[2x_{1}+3x_{32}-4x_{23}]=λ[0] ...λ[2x_{1}+3x_{32}-4x_{23}]=0 I think I just need a hint in the right direction. Thanks
The way I see it, you have one major problem- what you are trying to prove is not true! Now, please tell us the exact wording of the problem. I suspect you are misstating it.
I don't understand what you have above. Presumably x is a vector in R^{3}. Why are there two subscripts on some of the variables in your equation?
Ok sorry I did mistake the problem. it really should have said 2x_{1}+3x^{3}_{2}-4x_{3}^{2} I mistakenly read it as it was not typed out ver well and it appeared to look like weird subscript notation. and I solved it no problems Thanks for letting me know!