Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form a b c , where abc

This question is incomplete, the complete question is;

Determine if the described set is a subspace. Assume a, b, and c are real numbers.

The subset of R³ consisting of vectors of the form , where abc = 0

Therefore; The set is not a subspace

Step-by-step explanation:

Given the data the question;

the subset R³;

S = {   , where abc = 0 }

we know that a subset of R³ is a subspace if it stratifies the following properties;

Looking at the properties, we can say that it is not a subspace

As;

         u = ∈ S       and v =  ∈ S

As    1×1×0=0                          0×1×1=0

But   u+v =  ∉  S     as 1×2×1 ≠ 0

Hence, it is not closed under addition.

Therefore; The set is not a subspace

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