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Math Help - basis and linear dependence

  1. #1
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    basis and linear dependence

    Suppose S= \{v_{1}, v_{2}, ... v_{n}\} is a basis for vector space V, and T= \{w_{1}, w_{2}, ... w_{m}\} is a subset of V, where m > n. Show that T is linearly dependent.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by chickeneaterguy View Post
    Suppose S= \{v_{1}, v_{2}, ... v_{n}\} is a basis for vector space V, and T= \{w_{1}, w_{2}, ... w_{m}\} is a subset of V, where m > n. Show that T is linearly dependent.
    Hint:
    Spoiler:
    Pigeonhole principle
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    Hint:
    Spoiler:
    Pigeonhole principle
    Thanks. That's what I proved but I didn't know there was an actual name for it.
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