[理工] [線代]-六題證明題，請大家幫幫忙！
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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