A Hessenberg matrix H, is n X n matrix that has 2 on the main diaonal, 1 everywhere below the main diagonal and on the diagonal above the main one and zeros everywhere else. For example, 2 H2 = 1 1 1 H3 = 1 2 1 1 H4 = 1 1 0. 1 1 1 (1a, Compute det( H2) and det(H3). (1b, Compute det(H4) by doing the following steps: subtract column 2 from column 1 and use cofactor expansion along the resulting column 1 to show that det(H = det(H3) + det(H2). (1c, Follow the steps in (1b) to show that the same result holds for arbitrary n > 3 det(H det( I 1. 1. 1. 1. 1.

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