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Linear algebra

  1. Apr 5, 2006 #1
    Find a basis and calculate the dimension of the following subspaces of R4
    U = [a b c d] | a+b=c+d in R


    now a basis is supposed to be linear independant
    but that conditon on a,b,c,d makes this a bit strange

    can i just say d = a+b - c and then pick
    a basis as (1,0,0,1),(0,1,0,1),(0,0,1,-1)

    text says this however
    (-1,1,0,0),(1,0,1,0),(-1,0,0,1)

    please help
    i am currently studying for my exam i would like to understand everything!

    your help is greatly appreciated!
     
  2. jcsd
  3. Apr 5, 2006 #2

    0rthodontist

    User Avatar
    Science Advisor

    It looks like your text just chose to write a = d + c - b. I'm sure you know there can be more than one basis.
     
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