作者ruby791104 (阿年：）)
看板Grad-ProbAsk
标题[理工] [线代]六题证明题，请大家帮帮忙！
时间Wed Oct 28 21:01:13 2009
1.Is the transpose of an elementary matrix an elementary matrix of the
same type? Is the product of two elementary matrices an elementary matrix?
2.Let A be a 3x3 matrix and suppose that a1=3a2-2a3
Will the system Ax=0 have a nontrivial solution? Is A nonsingular?
3.Let A and B be nxn matrices and let C=A-B.
Show that if Ax0=Bx0 and x0≠0,then C must be singular.
4.Let A and B be nxn matrices and let C=AB.
Prove that if B is singular then C must be singular.
5.Show that if A is a symmetric nonsingular matrix,then A^-1 is also symmetric
6.Prove that if A is row equivalent to B,then B is row equivalent to A.
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1F：→ iyenn:作业吗?= =y 10/28 21:03
2F：→ iyenn:意思意思来个算一两题... 4.det(B)=0 ->det(C)=det(A)det(B) 10/28 21:14
3F：→ iyenn:C is singular. 10/28 21:14
4F：→ iyenn:3. (A-B)x=0=Cx -> x=/=0 ->C is singular. 10/28 21:15
5F：→ iyenn:5. A^T=A, (A^-1)^T=(A^T)^-1=A^-1 A^-1 is symmetric 10/28 21:17
6F：→ iyenn:6.E1E2...EkA=B Ek^-1...E2^-1E1^-1B=A 这样?,应该吧XD 10/28 21:19
7F：→ ruby791104:→谢谢你喔︿︿ 10/28 21:36