Q1 (10 points) 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, H2 - 7 2] 2 1 0 0 2 1 0 HA = 2 1 (1a, 4 marks) Compute det( H2) and det( H3). (1b, 4 marks) 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, 2 marks) Follow the steps in (1b) to show that the same result holds for arbitrary n 2 3 det(Hn) = det( Hn-1) + det( H,-2)