Linear Algebra Example Problems - Subspace Example #4

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We work with a subset of vectors from the vector space R2. We show that this subset of vectors is NOT a subspace of the vector space.

This problem is similar to Subspace Example #3, but the subset of R2 used in the problem is slightly different so the subspace criteria that pass/fail are slightly different as well.

Recall, in order for a subset of a vector space to be a subspace, it must satisfy three criteria:
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. In this problem, both 1) and 2) are true, but since 3) fails the subset of R2 is not a subspace of R2.

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