Determine every c Є R, for which the space [c,-1,-1], [2,3,c], [1,c,c] has dimension 2 I found out, that the D of matrix should be

Determine every c Є R, for which the space [c,-1,-1], [2,3,c], [1,c,c]  has dimension 2

I found out, that the D of matrix should be <>
My solution for matrix is: −c³+3⁢c²−c+3
So I tried the Gauussian elimination, but I got som weird fractions in matrix.
Don't know, how am I suppose to continue.


Will you help me please?
Thank you.