[理工] [線代]六題證明題，請大家幫幫忙！

[ruby791104 (阿年：）)]

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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◆ From: 210.240.186.200
→ iyenn:作業嗎?= =y
→ iyenn:意思意思來個算一兩題... 4.det(B)=0 ->det(C)=det(A)det(B)
→ iyenn:C is  singular.
→ iyenn:3. (A-B)x=0=Cx -> x=/=0 ->C is singular.
→ iyenn:5. A^T=A,  (A^-1)^T=(A^T)^-1=A^-1 A^-1 is symmetric
→ iyenn:6.E1E2...EkA=B Ek^-1...E2^-1E1^-1B=A 這樣?,應該吧XD
→ ruby791104:→謝謝你喔︿︿