Question: Is the given set, taken with the usual addition and scalar multiplication, a vector space? Give reason. If your answer is yes, find the dimension

Is the given set, taken with the usual addition and scalar multiplication, a vector space? Give reason. If your answer is yes, find the dimension and a basis.

All vectors in R³ satisfying -v₁ + 2v₂ + 3v₃ = 0, -4v₁ + v₂ + v₃ = 0

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