Re: [線代] 一些習題和觀念
※ 引述《Amulart (要衝刺!!!)》之銘言：
: 1.Let A and B be n*n matrices such that AB is invertible.
: Prove that A and B are invertible.
: 2.令 A 是 m*n 矩陣，且row rank(A) = k，當解 AX = 0 時 (X = ┌ x_1 ┐)
: │ x_2 │
: 為什麼具有 n-k 個自由變數？ │ . │
: │ . │
: │ . │
: 感謝各位解答!! └ x_n ┘
應該來搞個常見問題集
1) det(AB)=det(A)det(B)
A is invertible if and only if det A≠0
det(AB)≠0 if and only if det A and det B are both nonzero.
2)nullity +rank =n
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◆ From: 188.100.204.68
推
09/04 02:25, , 1F
09/04 02:25, 1F
推
09/04 16:22, , 2F
09/04 16:22, 2F
可以~~~意思是一樣的
A is one-to-one if and only if rank A=n when A is a square matrix.
rank(AB)=n if and only if both rank A and rank B are n.
n=rank(AB)≦min(rank A,rank B) => rank A=rank B = n
※ 編輯: herstein 來自: 195.37.209.182 (09/05 17:36)
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