作者mqazz1 (无法显示)
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标题[线代] N(A) = {0}, nonsingular
时间Sun Apr 17 23:38:21 2011
let A be an n*n matrix
prove that the following statements are equivalent
1.N(A) = {0}
2.A is nonsingular
3.for each b属於R^n, the system Ax=b has a unique solution
请问这要怎麽证呢?
谢谢
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※ 编辑: mqazz1 来自: 61.228.31.6 (04/17 23:39)
1F：推 yueayase :我不清楚定义是从什麽地方出发,不过你可以参考: 04/18 01:35
2F：→ yueayase :Linear Algebra with Applications by Steven J.Leon 04/18 01:35
3F：→ yueayase :他应该会直接证给你看 04/18 01:35
4F：推 powerkshs :N(A) = {0}→Ａ is 1-1，因为有限维，所以1-1→onto 04/18 10:31
5F：→ powerkshs :所以A is nonsingular 04/18 10:32
6F：→ powerkshs :因为A is nonsingular，所以A可逆，可逆→有唯一解 04/18 10:33
7F：→ powerkshs :应该就可以了 04/18 10:33