→ movo11:想請問一下第二題的(2) 10/16 22:21
推 wsx02:1.題目給AB=O? 這樣rank(AB)=0吧? 10/16 22:24
→ wsx02:2.(4)為True 10/16 22:24
→ Reylod:rank(AB) <= min(rank(A), rank(B)), 所以(2)不一定true 10/16 23:00
※ 編輯: movo11 來自: 59.127.250.83 (10/17 16:42)
1.Let A,B be 2x2 matrices over R with AB=0 and BA!=0 .
Determine the rank of BA.
2.Let A be m by n matrix,P be an inervertible m by m matrix,
and Q be an n by n matrix.
Which of the following is true?
(1)rank(AQ)=nullity(A)
(2)rank(AQ)=rank(A)
(3)rank(PA)=rank(P)
(4)rank(PA)=rank(A)
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