[理工] [線代]98交大資聯

[SkullMaster (SM)]

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

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◆ From: 111.248.224.211
→ ybite:p(x) = 5為一多項式，且其微分過後為0
→ ybite:我另有想法：如果以{1,x,x^2,x^3}為Basis，微分應該可表為
→ ybite:一個矩陣， [ 0 1 0 0 ]
→ ybite:        [ 0 0 2 0 ]
→ ybite:        [ 0 0 0 3 ]，其nullity=1，因此ker(D)!=0(歪了XD
→ ybite:        [ 0 0 0 0 ]
推 BenLinus:同意樓上!
→ peropero1:由定義：ker(D)={x|D(x)=0,x屬於P3},
→ peropero1:所以x需為常數才成立 所以ker(D)!=0
→ SkullMaster:我了解了,謝謝各位板指教:)