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.
--->R1 - R2
Apparently you don't know what "to reduce to echelon form means" , whether you use Gauss or Gauss-Jordan methods: you only have to make zeros every column below the upper one and "go down" from entry 1-1 to entry 2-2 and etc., until you reach the last row. Then you check under what conditions one row (many times the last one) becomes all zeroes...
Also, you could NOT have reached the above form for your matrix UNLESS you made some sharp assumption on h.