Let $V = \mathbb{R}^2$ and let $H$ be the subset of $V$ of all points in the first and third quadrants that lie between the lines $y = 2 x$ and $y = x / 2$. Is $H$ a subspace of the vector space $V$? Is $H$ nonempty? choose H is empty H is nonempty Is $H$ closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in $H$ whose sum is not in $H$, using a comma separated list and syntax such as $\verb+<1,2>, <3,4>+$. Is $H$ closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in $\mathbb{R}$ and a vector in $H$ whose product is not in $H$, using a comma separated list and syntax such as $\verb+2, <3,4>+$. Is $H$ a subspace of the vector space $V$? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3. choose H is a subspace of V H is not a subspace of V

In order to get credit for this problem all answers must be correct.