[理工] 線代

[KAINTS (RUKAWA)]

(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??

                         n    m
(3) Every function from R to R  has a standard matrix.
    F:要為linear transformation?

(4) A function is uniquely determined by the images of
    the standard vectors in its domain.
    F:不太懂原因

                       n    m
(5) Every function f: R -> R  preserves scalar mutiplication.
    F:要linear?

                n    m
(6)如果我們是T:R -> R ;其中m=\=n,有可能T is one-to-one and
   onto嗎??? 也就是說T反存在嗎? 我覺得是不存在...

感謝回答

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◆ From: 123.193.7.20
推 lion15945:應該是只限"一次"列運算吧? 好幾次就不叫列基本矩陣了
thx
※ 編輯: KAINTS          來自: 123.193.7.20         (11/05 14:05)
推 ILzi:我其實看不太懂第二題再說什麼耶..
→ ILzi:2p3是什麼東西？
A反中的第三行向量
※ 編輯: KAINTS          來自: 123.193.7.20         (11/05 15:29)
→ ILzi:我怎麼覺得我還是看不太懂題目...@@"
※ 編輯: KAINTS          來自: 123.193.7.20         (11/05 15:37)
→ KAINTS:i don't know either...
推 ILzi:有點好奇是誰出的？研究所考古題or補習班?
推 ILzi:算了，大概懂意思了 只是還是覺得題目表達不好
→ KAINTS:原文書
※ 編輯: KAINTS          來自: 123.193.7.20         (11/05 15:50)
推 ILzi:6.當然不存在..1-1 and onto只有在方陣才會存在
→ ILzi:這節去上完課回來沒人回答的話再來寫
推 ILzi:見下篇