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Show that this system is not a vector space

by charmedbeauty
Tags: space, vector
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charmedbeauty
#1
Jul25-12, 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 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
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HallsofIvy
#2
Jul25-12, 07:50 AM
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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.
Mark44
#3
Jul25-12, 01:12 PM
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P: 21,397
Quote Quote by charmedbeauty View Post
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?

charmedbeauty
#4
Jul26-12, 06:02 AM
P: 272
Show that this system is not a vector space

Quote Quote by HallsofIvy View Post
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 Quote by Mark44 View Post
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!


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