Let V R2 and lot H be the subset of V of all points on the

Let V = R^2 and lot H be the subset of V of all points on the line - 2x - 3y = 6. Is H a subspece of the vector space V? 1. Is H nonempty? 2. 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 , 3. 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, 4. Is H a subspace of the vector space You should be able to justify your answer by writing a company coherent, and detailed proof based on your answers to parts 1-3.

Solution

answer of problem 2 and 3 are wrong. for 2> answer is ,it is closed under addition so \"CLOSED\".For 3> write proper example one possible answer is 2, <-3, 0>.it is not a subspace because (0, 0) is not in subspace