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A set of 6 vectors in R5 cannot be a basis for R5, true or false?

  1. Aug 24, 2011 #1
    1. The problem statement, all variables and given/known data
    A set of 6 vectors in R5 cannot be a basis for R5, true or false?

    3. The attempt at a solution

    I'm thinking true, because any set of 6 vectors in R5 is linearly dependent, even though some sets of 6 vectors in R5 span R5.

    To be a basis it must be a linearly independent spanning set, so if it's linearly dependent, it cannot be a basis.
    Am I correct?
     
  2. jcsd
  3. Aug 24, 2011 #2

    Mark44

    Staff: Mentor

    Yes.
     
  4. Aug 24, 2011 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    A "basis" for a finite dimensional vector space has three properties:
    1. It spans the space.
    2. Its vectors are independent.
    3. The number of vectors in the basis is equal to the dimension of the space.

    And, if any two of these are true, so is the third.
     
  5. Aug 25, 2011 #4
    Thanks for the help.
     
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