Consider the set of (column) vectors defined by X = x...

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Consider the set of (column) vectors defined by X = {x \[ \in \] R³ | x₁ + x₂ + x₃ = 0, where x^T =[x₁, x₂, x₃]^T}. Which of the following is TRUE?

A. {[1, -1, 0]^T, [1, 0, -1]^T} is a basis for the subspace X

B. {[1, -1, 0]^T, [1, 0, -1]^T} is a linearly independent set, but it does not span X and therefore is not a basis of X

C. X is not a subspace for R³

D. None of the above

Answer: Option A

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