Suppose a 2 F, v 2 V, and av D 0. Prove that a D 0 or v D 0

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QUESTION:

Suppose a 2 F, v 2 V, and av D 0. Prove that a D 0 or v D 0.

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QUESTION:

Suppose a 2 F, v 2 V, and av D 0. Prove that a D 0 or v D 0.

ANSWER:

Step 1 of 3

If , then we immediately have our result.

So suppose . Then, because  is some nonzero real or complex number, it has a multiplicative inverse .

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