Let V R2 and let H be the subset of V of all points in the

Let V = [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 = 2x and y = x/2. Is H a subspace of the vector space V? Does H contain the zero vector of V? H contains the zero vector of V 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 , . Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H whose product is not in H, using a comma separated list and syntax such as 2, . 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. H is a subspace of V

Solution

Since H is not closed under addition H is not a subspace for vector space V.

The zero vector for V is <0,0> and for H it is the same, so contain the zero vector of V