A Hessenberg matrix Hn 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, 1 H2 = 1 2 2 1 H3 = 1 2 1 1 1 2 1 0 0 1 HA = 1 2 1 1 1 1 1 1 2. (1а, 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(H4) = det(H3)+ det(H2). (1c Follow the steps in (1b) to show that the same result holds for arbitrary n 2 3 det(Hn) = det(H,n-1) + det(Hn 2). %3D

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