Let v be a vector and let k be a scalar. From the axioms of a vector space, prove that if kv = 0 theneither k = 0 or v = 0.

Question

Let v be a vector and let k be a scalar. From the axioms of a vector space, prove that if kv = 0 theneither k = 0 or v = 0.
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Solution 1

To prove this, we will use the axioms of a vector space and the properties of scalar multiplication.

Step 1: Assume that kv = 0 for some scalar k and vector v.

Step 2: We have two cases to consider: k = 0 or k ≠ 0.

Case 1: If k = 0, then we have 0v = 0, which is true by the zero scalar multiplic Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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