[線代] 一題線代

[tim8238818 (AAAAAAAAAAAAAAAAAAAAAAA)]

Let A and B be such that AB is defined. Prove that if B has two identical
  columns, then AB also has two identical columns.

這題如果要我假設任何column等於0我就會證了
其實我是不太了解identical column的意思
這樣我不知道從哪裡下手@@


先謝謝板上神人賜教...

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◆ From: 173.198.43.204
※ 編輯: tim8238818      來自: 173.198.43.204       (03/11 10:05)
推 joehuan     :假設B是mxn, e_i是nx1的單位向量, 第i是1,其他0
推 Linethan    :就是指B有兩個行一模一樣
→ joehuan     :B有兩個一樣的column,所以我可以找到j,k in 1,2...n
→ Linethan    :AB=A(b1,b2,...,bn)=(Ab1,Ab2,...,Abn)
→ joehuan     :j!=k, 讓Be_j=Be_k
→ Linethan    :IF b1=b2, then Ab1=Ab2. AB has two identical colu
→ joehuan     :ABe_j=A(Be_j)=A(Be_k)=ABe_k, AB有兩個一樣的column