Real Euclidean Space
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Consider the following subset B of R^3 (real Euclidean space):
B={(x,y,z) in R^3 such that x=y+z}
With the usual "component wise" addition and scalar multiplication in R^3, is B a vector space? Prove or disprove your answer.
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Solution Summary
Real Euclidean Space is depicted.
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Proposition: The subset B <= R^3 with B = {(x, y, z)|x = y + z|} is a vector subspace of R^3.
Proof: We will show that B is ...
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