作者mqazz1 (無法顯示)
看板Math
標題[線代] N(A) = {0}, nonsingular
時間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屬於R^n, the system Ax=b has a unique solution
請問這要怎麼證呢?
謝謝
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◆ From: 61.228.31.6
※ 編輯: mqazz1 來自: 61.228.31.6 (04/17 23:39)
1F：推 yueayase :我不清楚定義是從什麼地方出發,不過你可以參考: 04/18 01:35
2F：→ yueayase :Linear Algebra with Applications by Steven J.Leon 04/18 01:35
3F：→ yueayase :他應該會直接證給你看 04/18 01:35
4F：推 powerkshs :N(A) = {0}→Ａ is 1-1，因為有限維，所以1-1→onto 04/18 10:31
5F：→ powerkshs :所以A is nonsingular 04/18 10:32
6F：→ powerkshs :因為A is nonsingular，所以A可逆，可逆→有唯一解 04/18 10:33
7F：→ powerkshs :應該就可以了 04/18 10:33