Sorry for the long post but I'm really stuck with this problem. I have to find all of the h values for which this matrix is invertible. I tried to find the inverse so that explains extra 4 columns. I've asked this question before and i was suggested to use a determinant but the problem is we haven't learned any formulas for the determinant yet except for the 2*2 matrix. I reduced it to echelon form but i don't know what to do next.

--->R2-R3

----> R1-R3

----> R3-R2

--->R1 - R2

---> R3-R4

--->R3/2 +R4

--->2R3 +6R4

--->R4/3& (R3/2h+R1