[理工] 線代 線性映射
想請問這兩題的題意差在哪裡？
Let P3 be the vector space of all polyminals of degree
less than 3. Let E = [1,x+1,x^2] and F = [1,x,1+x+x^2]
be two ordered bases of P3.
If A is the transition matrix representing the change of
coordinates from the ordered basis E to the ordered F,
then A = _.
這題我用 E = F A 可以求出答案
Find the transition matrix representing the change of
coordinates on P3, P3跟上題一樣, from the basis
a = [1,x,x^2] to the basis b = [1,1+x,1+x+x^2].
這題我用a = b A (A為transition matrix)
算出A是
[ 1 1 1 ]
[ 0 1 1 ]
[ 0 0 1 ]
答案卻是
[ 1 -1 0 ]
[ 0 1 -1 ]
[ 0 0 1 ]
麻煩各位了
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◆ From: 140.115.207.144
推
11/16 00:19, , 1F
11/16 00:19, 1F
→
11/16 00:20, , 2F
11/16 00:20, 2F
→
11/16 00:23, , 3F
11/16 00:23, 3F
→
11/16 00:31, , 4F
11/16 00:31, 4F
→
11/16 00:31, , 5F
11/16 00:31, 5F
推
11/16 15:01, , 6F
11/16 15:01, 6F
→
11/16 15:01, , 7F
11/16 15:01, 7F
→
11/16 15:01, , 8F
11/16 15:01, 8F
第一題我的想法是這樣
假設x屬於P3 可以由E與F空間中的元素組合出來
x = E Xe = F Xf Xe 和 Xf是 x在E的基底和F的基底上的座標
F^-1 E Xe = Xf 令A = F^-1 E
所以 E = F A
那同理第二小題
a = b A
還是標準基底有什麼特色我沒注意到？
還請版友指教 謝謝
推
11/16 15:23, , 9F
11/16 15:23, 9F
可以分享一下嗎XD 感謝你!
※ 編輯: TangHsing 來自: 140.115.207.144 (11/16 18:18)
→
11/16 22:18, , 10F
11/16 22:18, 10F
→
11/16 22:20, , 11F
11/16 22:20, 11F
我知道我錯在哪了.....
我寫a=bA 卻算aA=b....
我好蠢= =
※ 編輯: TangHsing 來自: 118.165.21.94 (11/17 11:36)
→
11/17 12:19, , 12F
11/17 12:19, 12F
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