If V is a vector space and for all vectors v and w in V, then V consists of only the zero vector.

Name: If V is a vector space and for all vectors v and w in V, then V consists of only the zero vector.
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Question

If V is a vector space and  for all vectors v and w in V, then V consists of only the zero vector.

Quizplus · Accepted Answer

The only vector v such that ||v||=0 is the zero vector. Therefore, if ||v+w||=0 for all vectors v and w in V, then v+w must be the zero vector, which implies that V consists of only the zero vector.

If V Is a Vector Space and for All