Basically, I'm having student look for the x that makes the matrix
singular, or the columns linearly dependent, or ...  However Sage
behaves like so:

sage: A=matrix([[0,1,1],[2,2,-2],[-1,x,3]])
sage: A
[ 0  1  1]
[ 2  2 -2]
[-1  x  3]
sage: A.echelon_form()
[1 0 0]
[0 1 0]
[0 0 1]


Is there anyway to make it so Sage doesn't assume that it can rescale
by dividing by whatever function of x we get in the bottom row (in
this case 1-x), because that might be 0?

Doing the row reduction 'by hand', ie making Sage do it, works, but it
would be nice if echelon form did it.

Thanks,

Matt
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