Let be defined as .
Determine whether is a subspace of under the usual vector addition and scalar multiplication.

Question

Let    be defined as   . 
 Determine whether    is a subspace of    under the usual vector addition and scalar multiplication.

Answer

No,     is not  a subspace because it is not closed under addition.

Answer

Yes,     is  a subspace.

Answer

No,     is not  a subspace because it does not contain the zero vector.

Answer

No,     is not  a subspace because it is not closed under scalar multiplication.

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