[代數] Cosets
1. In the additive group |R^m of vectors, let W be the set of solutions
of a system of homogeneous linear equations AX=0. Show that the set
of solutions of an inhomogeneous system AX=B is either empty or
it is an (additive) coset of W
首先這題的A應該是個方陣吧?!
那麼AX=B無解的話，表示set of solution of AX=B is empty.
若是以這樣的想法，我想不出如果有solution的話，和coset會有甚麼關係.....
2. A group G of order 22 contains elements x and y, where x≠1 and y is not
a power of x. Prove that the subgroup generated by these elements in the
whole group G.
依照題意我覺得會用到cyclic group，但是不知道從何下手......
感謝各位大大指教 :)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 125.225.15.246
推
10/30 22:54, , 1F
10/30 22:54, 1F
→
10/30 22:54, , 2F
10/30 22:54, 2F
推
10/31 03:44, , 3F
10/31 03:44, 3F
→
10/31 03:44, , 4F
10/31 03:44, 4F
→
10/31 03:45, , 5F
10/31 03:45, 5F
→
10/31 03:46, , 6F
10/31 03:46, 6F
→
10/31 03:46, , 7F
10/31 03:46, 7F
→
10/31 11:13, , 8F
10/31 11:13, 8F