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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
- The set is a subspace
- The set is not a subspace
Answer:
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;
- it contains additive identity
- it is closed under addition
- it is closed under scales multiplication
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