- #1

charmedbeauty

- 271

- 0

## Homework Statement

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}

## Homework Equations

## 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