Chapter 4 - Vector Spaces - 4.11 Chapter Review - Additional Problems - Page 336: 15

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Let $V$ be a vector space of problem 14. Assume the set $S=\{(1,2);(3,8)\}$ Since $(1,2)=(1,2^1) \\ (3,8)=(3,2^3) \rightarrow S \subset V$ By problem 14 we have $(0,1)$ is the zero vector of $V$. Take $-3(1,2)+1(3,8)=(-3, 2^{-3})+(3,2^3)=(0,1)$ Hence, $S$ is a subspace of the vector space $V$ given in problem 14