[理工] [線代]-98交大資聯

看板Grad-ProbAsk作者 (SM)時間13年前 (2011/02/11 15:55), 編輯推噓1(1推 0噓 9→)
留言10則, 4人參與, 最新討論串1/1
98交大資聯 線代 5.選對的 (c) Let P3 be the space consisting of all polynomial of degree no more than 3, and D be the differetiation operator on P3 . Then, ker(D) = {0}. 這選項是錯的 有板友能提供一點想法嗎? 感謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.248.224.211
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02/11 16:01, , 1F
p(x) = 5為一多項式，且其微分過後為0
02/11 16:01, 1F
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02/11 16:02, , 2F
我另有想法：如果以{1,x,x^2,x^3}為Basis，微分應該可表為
02/11 16:02, 2F
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02/11 16:03, , 3F
一個矩陣， [ 0 1 0 0 ]
02/11 16:03, 3F
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02/11 16:03, , 4F
[ 0 0 2 0 ]
02/11 16:03, 4F
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02/11 16:03, , 5F
[ 0 0 0 3 ]，其nullity=1，因此ker(D)!=0(歪了XD
02/11 16:03, 5F
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02/11 16:04, , 6F
[ 0 0 0 0 ]
02/11 16:04, 6F
推
02/11 16:44, , 7F
同意樓上!
02/11 16:44, 7F
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02/11 17:35, , 8F
由定義：ker(D)={x|D(x)=0,x屬於P3},
02/11 17:35, 8F
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02/11 17:35, , 9F
所以x需為常數才成立 所以ker(D)!=0
02/11 17:35, 9F
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02/11 17:43, , 10F
我了解了,謝謝各位板指教:)
02/11 17:43, 10F
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