Suppose you have an nxn matrix with 0s on the diagonal and at least one 1 on every row. Does this matrix have a determinant? @ganeshie8 @ikram002p @dan512

Question

kainui · Answer

Ahhh... damn I just came up with a counter example. Oh well.

ganeshie8 · Answer

i think we can choose some permutation matrix as counter example :

1 0 0
0 1 0
0 0 1

and

0 0 1
1 0 0
0 1 0

determinant cannot be zero as both represent same system

rvc · Answer

why not?

kainui · Answer

Yes however @ganeshie8 

0 1 1
0 0 0
1 0 0

This meets my requirements unfortunately.

perl · Answer

what do you mean both represent same system?

perl · Answer

@ganeshie8  what do you mean both represent same system.
and what does a determinant not exist. you can always find a determinant

ganeshie8 · Answer

I think Kainui means non-zero-determinant @perl

ganeshie8 · Answer

matrices listed in previous reply represent coefficient matrix of same system of equations : 

```
x       = a
   y    = b
      z = c
``

kainui · Answer

Yeah, that's exactly what I meant. I was thinking "does not have an inverse" and "has determinant of zero" at the same time and they both came out haha