Question: For i = 1, 2, ..., n, let Ai, Bi, Ci ( (i and set E = A1 ..., An, F = B1 ...

For i = 1, 2, ..., n, let Ai, Bi, Ci ( (i and set E = A1 ×...×, × An, F = B1 ×...× Bn, G = C1 ×...× Cn. Suppose that E, F, and G are all ( ( and that E = F + G. Then show that there exists a j with 1 ≤ j ≤ n such that A j = B j + C j while Ai = Bi = Ci for all i ( j.

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We have E F G and E F G are all This implies that A i B i and C i i 1 n are all this is so by Exercise 16 i Furthermore by Exercise 16 ii F G B 1 B n C 1 C n B 1 C 1 B n C n whereas F G It follows tha... View full answer

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