I have to find the 4-dimensional volume of {s'(adsbygoogle = window.adsbygoogle || []).push({}); v'+ s''v''+ s'''v'''+s''''v'''': 0<= s',s'',s''',s'''' <=1 }

in R^7, wherev'= (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?

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# Homework Help: 4-dimensional volume

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