Let V = R³ and let H be the subset of V of all points on the plane 5x - 4y + 7z = -20. Is H a subspace of the vector space V?
1. Does H contain the zero vector of V?
H does not contain the zero vector of 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>, <4,5,6>.
CLOSED
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, <3,4,5>
CLOSED
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 a subspace of V