Originally Posted by

**mivanova** Hi, Thanks for the help before.

Can you help me with this new problem.

Define the following determinants of the matrices whose elements come from the ring F[x]:

δ1=1

δ2= | 0 -1|

|-1 x|

δ3= | 0 -1 0|

| 0 x -1|

|-1 0 x|

δ4= | 0 -1 0 0|

| 0 x -1 -1|

| 0 0 x -1|

|-1 0 0 x|

Continue in this fashion. δn is the determinant of an nxn matrix each of whose entries is either 0 or -1 or x according to the following rule. The diagonal entries are all equal to x except for the first diagonal entry which is 0. Each entry along the super diagonal, (i.e. just above the main diagonal) equals -1, as does the entry in the lower left-hand corner. All other entries are 0. Evaluate δn.

Thank you!