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Show that this system is not a vector space 
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#1
Jul2512, 07:09 AM

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 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 


#2
Jul2512, 07:50 AM

Math
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Sci Advisor
Thanks
PF Gold
P: 39,345

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. 


#3
Jul2512, 01:12 PM

Mentor
P: 21,215




#4
Jul2612, 06:02 AM

P: 272

Show that this system is not a vector space
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! 


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