Please answer following the same format and box the correct answer. Do not type out the answer. Chapter 3.2 Question 3 , .3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is...

Please answer following the same format and box the correct answer. Do not type out the answer.

Chapter 3.2 Question 3

Extracted text: Let V = R? and let H be the subset of V of all points on the line -4x + 3y = -12. Is H a subspace of the vector space V? 1. Is H nonempty? H is nonempty v 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 <1,2>, <3,4>. 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, <3,4>. 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. H is not a subspace of V v