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Linear Algebra

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Vector Space Operations

LINALG-XDYLEB

A vector space $V$ is a nonempty set of objects called vectors on which are defined operations.

Which of the following statements are TRUE?

A

For $V$ to be a vector space there are two operations that must be defined on $V$. One of these combines two vectors in $V$ to get another vector in $V$ and is called vector addition. The other combines a real number and an element of $V$ to get another element in $V$, this operation is called multiplication by a scalar.

B

Every vector space $V$ has two operations defined on $V$. One is addition of elements in $V$ and the other is multiplication of elements in $V$.

C

Both of the above are true.

D

None of the above are true.