[線代] N(A) = {0}, nonsingular

看板Math作者 (無法顯示)時間15年前 (2011/04/17 23:38), 編輯推噓2(2推 0噓 5→)
留言7則, 2人參與, 最新討論串1/1
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 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.31.6 ※ 編輯: mqazz1 來自: 61.228.31.6 (04/17 23:39)
推
04/18 01:35, , 1F
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, 1F
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04/18 01:35, , 2F
Linear Algebra with Applications by Steven J.Leon
04/18 01:35, 2F
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04/18 01:35, , 3F
他應該會直接證給你看
04/18 01:35, 3F
推
04/18 10:31, , 4F
N(A) = {0}→Ａ is 1-1，因為有限維，所以1-1→onto
04/18 10:31, 4F
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04/18 10:32, , 5F
所以A is nonsingular
04/18 10:32, 5F
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04/18 10:33, , 6F
因為A is nonsingular，所以A可逆，可逆→有唯一解
04/18 10:33, 6F
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04/18 10:33, , 7F
應該就可以了
04/18 10:33, 7F
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