(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Show that this system is not a vector space

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