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]]

Expert Answers
rakesh05 eNotes educator| Certified Educator

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.

pramodpandey | Student

The augmented matrix has no trivial solution. ie.

        1   c-1     1

 D=   0     c     4

        1      c   c+1

By elementry row operation

      1    c-1   1

D = 0     c     4

       0      1    1

If we expand this  then det (d)=C^2-4

for non trivial solution we have Det(D)=0