What are the values of c? The follwing system is an augmented matrix that has no trivial solutions. [[1,c-1,1,|,0],[0,c,4,|,0],[1,c,c+1,|,0]]
If the augmented matrix has no trivial solution then we cannot find the value of c in the real field. As it is coming c^2+4=0 i.e. c=+-(2i).
If we prepare the augmented matrix and reduce by elementary operations we get 4-c^2=0 or c=+2 and c=-2.
For above values of c, the system has no trivial solutions. As we are getting a 2by2 matrix for three variables.