If X and Y are subsets of a vector space, and either X or Y is linearly dependent, show thatX ∪ Y is linearly dependent.

Question

If X and Y are subsets of a vector space, and either X or Y is linearly dependent, show thatX ∪ Y is linearly dependent.
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Solution 1

To prove that the union of two subsets X and Y of a vector space is linearly dependent if either X or Y is linearly dependent, we can follow these steps:

  1. Assume without loss of generality that X is the set that is linearly dependent. This means that there exists a non-trivial linear combination Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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