<Dl> <Dd> V o l (P) = d e t ((V 0 1) T, (V 1 1) T,..., (V n 1) T), (\ displaystyle (\ rm (Vol)) (P) = (\ rm (det)) \ ((V_ (0) \ 1) ^ (\ rm (T)), (V_ (1) \ 1) ^ (\ rm (T)), \ ldots, (V_ (n) \ 1) ^ (\ rm (T))),) </Dd> </Dl> <Dd> V o l (P) = d e t ((V 0 1) T, (V 1 1) T,..., (V n 1) T), (\ displaystyle (\ rm (Vol)) (P) = (\ rm (det)) \ ((V_ (0) \ 1) ^ (\ rm (T)), (V_ (1) \ 1) ^ (\ rm (T)), \ ldots, (V_ (n) \ 1) ^ (\ rm (T))),) </Dd> <P> where (V i 1) (\ displaystyle (V_ (i) \ 1)) is the row vector formed by the concatenation of V i (\ displaystyle V_ (i)) and 1 . Indeed, the determinant is unchanged if (V 0 1) (\ displaystyle (V_ (0) \ 1)) is subtracted from (V i 1) (\ displaystyle (V_ (i) \ 1)) (i> 0), and placing (V 0 1) (\ displaystyle (V_ (0) \ 1)) in the last position only changes its sign . </P> <P> Similarly, the volume of any n - simplex that shares n converging edges of a parallelotope has a volume equal to one 1 / n! of the volume of that parallelotope . </P>

Describe the translation in the figure from a to a'. a. b. c. d