Linear Algebra Example Problems – Subspace Example #2

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We work with a subset of vectors from the vector space R3. We show that this subset of vectors is NOT a subspace of the vector space.

In general, given a subset of a vector space, one must show that all of the following are true:

1) Contains the zero vector, 2) Is closed under addition, and 3) Is closed under scalar multiplication.

If any of these fail, the subset is not a subspace. It turns out that for the particular example worked in this problem none of these properties are true.

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