# 關於線性代數的問題 "

誰能幫我證明順便解釋以下的定理(用數學歸納法證明喔!!!)

Theorem:[Replacement Theorem]

Let V be a vector space that is generated by a set G containing exactly n elements, and let L be a linearly independent subset of V containing exactly m elements. Then m<n or m=n and there exists a subset H of G contains n-m elements such that LUH generates V.

Update:

我也會解釋= =不過我要的是證明~還是謝謝妳喔^^

### 1 Answer

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- Anonymous1 decade agoFavorite Answer
我不會証（小的也剛學）～可是我會解釋那個定理～～

那是代換定理

Let span(G)=V 使得|G|=n

且L是存在於V的一個子空間且線性獨立

m>n or m=n

且存在一個H屬於G =>|H|=n-m 使得L與H的聯集之生成集為V

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