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Let be the set of all points in the first and third quadrants
in the plane .
That is, .
Is a subspace of the vector space ?
- Does contain the zero vector of ?
- 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.
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