[理工] [線代]線性映射

[dkcheng (電磁霸主)]

                                 2                   2    2
    An affine transformation of R  is a function T: R → R  of the form

                                                         2
T(x)=Ax+b, where A is an invertible 2x2 matrix and b屬於R . Which of the


following statements are correct ?

     -1     -1   -1
(A) T  (x)=A  x-A  b


(B) Affine transformations map straight lines to straight lines.


(C) There is no affine transformation that can map a straight line to a circle


(D) Affine transformations map parallel straight lines to parallel straight

lines.

(E) There exists an affine transformation that maps parallel straight lines

to intersecting straight lines.


覺得這題頗難的...

麻煩各位了


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推 harrypotter2:A is invertible←→1-to-1 & onto
→ harrypotter2:(A)x用Ax+b代可得x :True
→ harrypotter2:(B)因A為1-to-1 & onto ,故維數一樣 :True
→ harrypotter2:(C)圓是1對多  :False
→ harrypotter2:(D)y=ax+b代入可知 :True
→ harrypotter2:(E)dim(平行線)≠dim(交叉線)  :False
→ harrypotter2:有錯請指正...謝謝
→ gskman:這...我的答案選的是A E說XD
推 harrypotter2:尷尬了XD  幫忙指正錯誤  感謝
推 harrypotter2:發現(D)有錯 忘了外面的常數b導致他們不平行...
→ gskman:說不定是我想錯了XD
推 harrypotter2:所以(E)是對的...
推 gskman:我決定要訂正我的答案了XD ABCD
→ feabries:請問一下 b會=0嗎?
推 w29697146:我記得線性映射會把零向量傳到零向量 所以b應該只能為
→ w29697146:零向量
推 harrypotter2:難怪題目只說是映射轉換...
推 gskman:b不用等於0阿 這題是Affine 不是linear喔
推 w29697146:拍謝 沒仔細看題目@@
推 harrypotter2:(C)圓是1對多 :True       沒看到no
推 genius945:可以問一下這是哪張的嗎..怎沒讀到Affine..死定了= =
→ harrypotter2:所以答案是(A)(B)(C)(D)  常數不影響方向 剛昏頭了..
推 harrypotter2:感覺是線性映射的延伸
→ say19880920:abcd +1
推 gskman:affine 其實跟linear差不多 看題目怎麼給 後面的b是上下
→ gskman:左右的橫移
→ gskman:A就是拉長縮短轉角度這樣,不過一般的性質還是差不多
推 mp8113f:True : ABCD    False : E
→ dkcheng:答案是(A)(B)(C)(D)..有沒有人會用數學推導的 ?
→ dkcheng:不要直接看
→ sneak: 我記得線性映射會把零向 https://daxiv.com