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4-dimensional volume

  1. Oct 22, 2005 #1
    I have to find the 4-dimensional volume of {s'v' + s''v'' + s'''v''' +s''''v'''': 0<= s',s'',s''',s'''' <=1 }

    in R^7, where v' = (1,1,0,1,0,0,1)^T,
    v''=(1,0,0,1,1,0,0)^T
    v'''=(0,0,1,1,1,0,0)^T
    v''''=(0,0,0,0,1,1,1)^T


    So I decided to try and take the determinant of the matrix which holds these vectors, by expanding along the 1st row consisting of elementary coordinates.

    | e1 e2 e3 e4 e5 e6 e7 |
    | 1 1 0 1 0 0 1 |
    | 1 0 0 1 1 0 0 |
    | 0 0 1 1 1 0 0 |
    | 0 0 0 0 1 1 1 |


    But, ummm... as you might already know, it doesn't work out. What do I do?
     
  2. jcsd
  3. Oct 22, 2005 #2
    clarifying, all the s,v are scalars, vectors respecively...by "^T", i just meant to write transpose...
     
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