Sometimes matrices of a certain form have inverses of a certain form. Consider an n n matrix with 0s everywhere, except 1s on the main diagonal, and the diagonal immediately above the main diagonal, for example: .

(a) Use the Matlab inv(n) function to find the inverse of the four matrices above.

(b) What special form, if any, do the inverses have? Be specific.

Your answer here should be a Matlab diary or script for part (a) showing how you entered or constructed the matrices, the statement finding the inverse, and then the Matlab output for each. You answer for part (b) should be a typed description of inverses form. Make sure to include all this in your Matlab submission file.

1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 (1 1). 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0