Re: [理工] 線代

[ILzi ( 並不好笑 )]

※ 引述《KAINTS (RUKAWA)》之銘言：
: (1) An elementary matrix is a matrix that can be obtained by
:     a sequence of elementary row operations on an identity
:     matrix.
:    F:看不出來錯在哪...
: (2) Suppose that A is an invertible matrix and u is a solution
:                     T                               T
:     of Ax=[ 5 6 7 8] . The solution of Ax=[ 5 6 7 8 ] differs
:                                                    -1
:     from u by 2p3,where p3 is the third column of A  .
:     T:要怎麼證明??
           -1
[A|I]→[I|A  ]
   -1
令A  =[A1 A2 A3 A4]
所以我們可以知道

u = 5A1 + 6A2 + 7A3 + 8A4
而新的解則是
v = 5A1 + 6A2 +14A3 + 8A4

因為A可逆，所以A3≠0

=> u≠v..
:                          n    m
: (3) Every function from R to R  has a standard matrix.
:     F:要為linear transformation?
   3   2
T:R →R
T(u)=0
      [1 1 1]      [1 1 1]
則取A=[2 2 2]和取B=[3 3 3]會有同樣的結果
所以並沒有所謂standard matrix
: (4) A function is uniquely determined by the images of
:     the standard vectors in its domain.
:     F:不太懂原因
我想問題在於standard vector...
何謂標準向量？
:                        n    m
: (5) Every function f: R -> R  preserves scalar mutiplication.
:     F:要linear?
    n
f：R →R
f(u)=Σui = [1 1 1 1 ... 1]u
則f不用有scalar mutiplication..
: 感謝回答
不敢保證一定都對
請大家幫忙訂正
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◆ From: 163.19.249.253
推 KAINTS:第一個疑問v的第三項不是7-2=5嗎?? 第二個我還是不懂這在問
→ KAINTS:什麼....
→ ILzi:differ from是不同於，不是"減"
→ ILzi:把p3乘2之後的解會和u不同
推 KAINTS:喔喔，懂了，thx
※ 編輯: ILzi            來自: 163.19.249.253       (11/05 17:48)
※ 編輯: ILzi            來自: 163.19.249.253       (11/05 17:50)
推 bouwhat:想請問第一題
→ ILzi:第一題請見上篇第一推..
推 bouwhat:ok感謝