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Math proof

  1. Sep 27, 2016 #1
    1. The problem statement, all variables and given/known data
    Show that any vector in a vector space V can be written as a linear combination of a basis set for that same space V.


    2. Relevant equations
    http://linear.ups.edu/html/section-VS.html
    We are suppose to use the 10 rules in the above link, plus the fact that if you have a lineraly independent set
    {X1,X2,...,Xn} then -> c1X1+c2X2+...+cnXn = 0 vector implies that all the constants (c1,c2, etc) are zero.

    Not looking for a complete solution, just not sure where to start. Ive tried proof by contradiction and a couple other ways and non have worked out for me.

    3. The attempt at a solution
     
  2. jcsd
  3. Sep 28, 2016 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Define "basis". (I know the usual definition, but what is the one YOU are using?)
     
  4. Oct 5, 2016 #3
    My definition is a linearly independent set of N vectors, where N in the dimension of the space. My definition of dimension, N, is it the max number of mutually lineraly independant vectors possible.
     
  5. Oct 5, 2016 #4

    fresh_42

    Staff: Mentor

    So what can you say about a given vector? Can it be linearly independent from your basis? Or otherwise, what does it mean it can't?
     
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