# Show that this system is not a vector space

by charmedbeauty
Tags: space, vector
 P: 272 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 ℝ3 S={x(ℝ3):2x1+3x32-4x23=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[2x1+3x32-4x23]=λ[0] ...λ[2x1+3x32-4x23]=0 I think I just need a hint in the right direction. Thanks
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 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.
Mentor
P: 21,397
 Quote by charmedbeauty 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 ℝ3 S={x(ℝ3):2x1+3x32-4x23=0}
I don't understand what you have above. Presumably x is a vector in R3. Why are there two subscripts on some of the variables in your equation?

P: 272
Show that this system is not a vector space

 Quote by HallsofIvy 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.
 Quote by Mark44 I don't understand what you have above. Presumably x is a vector in R3. 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 2x1+3x32-4x32

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!

 Related Discussions Linear & Abstract Algebra 6 Linear & Abstract Algebra 12 Calculus & Beyond Homework 9 Calculus & Beyond Homework 5 Calculus & Beyond Homework 1