[線代] 一些習題和觀念

[Amulart (要衝刺!!!)]

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 ┘

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◆ From: 140.117.36.24
推 YINGLANG    :1用 n*n矩陣M可逆 iff rank(M)=n
→ YINGLANG    : 跟 rank(AB)小於等於rank(A)跟rank(B)
→ Sfly        :1.  (AB)C=C(AB)=I  =>  A(BC)=I & (CA)B=I.