Linear Algebra Example Problems - Subspace Example #1
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We work with a subset of vectors from the vector space R3. We show that this subset of vectors is a subspace of the vector space via a useful theorem that says the following:
Given a vector space V, the span of any set of vectors from V is a subspace of V.
Since we're able to write the given subset of vectors as the span of vectors from R3, the set of vectors in this problem is indeed a subspace of R3.
Another way to work this problem is to show that the set of vectors satisfies the following 3 properties: 1) Contains the zero vector, 2) Is closed under addition, and 3) Is closed under scalar multiplication.
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