[理工] [線代]99台大電機

[bouwhat (微笑的故事)]

大家好，想請教兩題99台大電機的題目
1、suppose that V and W are finite dimentional vector space and that U is a subspace of V.Then there exist a linear transformation T from V to W,such that null(T)=U if and only if dim(U)>=dim(V)-dim(W)
2.suppose T is n*n matrix.Then T is a scalar multiple of the n*n identity matrix if and only if ST=TS for every n*n matrix S

兩題都是true

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→ sting47:你的問題是...?
推 ILzi:應該是true的證明吧..
→ bouwhat:sorry沒講清楚要問什麼
→ bouwhat:第一題我會了
→ bouwhat:想請教第二題的題意
→ sting47:應該是 (雙向)if T=cI(c是係數)則for all S ST=TS
→ bouwhat:懂了感謝！