Is there such a thing as a matrix without pivot positions?

Question

Is there such a thing as a  matrix without  pivot positions?

amistre64 · Answer

as is,   yes

amistre64 · Answer

2   3
4  -1

as is, has no pivot positions, but if we are meant to relate this to its row reduced form, then maybe

amistre64 · Answer

can you think of a matrix (does it have to be nxn?) that doesnt reduce to an echelon form?

anonymous · Answer

well  2 4
       3 6                     0 0
would reduce down to 3 6.  
but I'm struggling with trying to show a 2x2 case generally that doesn't have leading ones but dont know where to start.. or if I even can. Ultimately, i'm trying to prove something by contradiction.

anonymous · Answer

oops that's supposed to be 24
                                         36

and 00
       36.