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xkehaulanix

  • 4 years ago

True or False? If a set in R^n is linearly dependent, then the set contains more vectors than there are entries in each vector. Gut instinct said true according to a theorem stating that a set with more vectors than entries in each vector is linearly dependent. Then another gut instinct said I was wrong.

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  1. TuringTest
    • 4 years ago
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    (1,1)(2,2) are linearly dependent and don't have that issue, so linear dependency does not imply more vectors than entries unless you only consider reduced form...

  2. TuringTest
    • 4 years ago
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    ...I think

  3. xkehaulanix
    • 4 years ago
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    ...Well since you found a counterexample, I'd say you're pretty spot on. Thanks!

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