(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that S = {(a+1,b,0)|a,b are real numbers} is NOT a subspace of R^3.

2. Relevant equations

3. The attempt at a solution

I take a specific counter example:

Let k = 0 inside real, and u = (1+1,1,0) inside S

ku = 0(1+1,1,0) = (0,0,0) not inside S

So, S is not a subspace.

[I can let k = 0 right? Because 0 is also a real number]

Another counter example:

Let u = v = (-1+1,1,0) inside S

u + v = (0,2,0) not inside S

So, S is not a subspace.

Which of the counter examples should I use? It seems that the first one makes more sense to me. The second one is really weird.

Thanks.

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# Linear Algebra - Subspace

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