Let and let be the subset of of all points on the plane . Is a subspace of the vector space ?
Is nonempty?
choose
H is empty
H is nonempty
Is closed under addition? If it is, enter
CLOSED
. If it is not, enter two vectors in whose sum is not in , using a comma separated list and syntax such as .
Is closed under scalar multiplication? If it is, enter
CLOSED
. If it is not, enter a scalar in and a vector in whose product is not in , using a comma separated list and syntax such as .
Is a subspace of the vector space ? 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.