1. Is H nonempty- Yes, H is 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 <1,2,3>, <4,5,6>. - It is 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>. - It is 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 not a subspace of V. A Subspace is a Vector Space included in another larger Vector Space. Therefore, all properties of a Vector Space, such as being closed under addition and scalar multiplication still hold true when applied to the Subspace.
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