***** original matrix *****
        1.00        2.00      300.00        4.00        5.00
        2.00        3.00      400.00        5.00        6.00
        3.00        4.00        5.00        6.00        7.00
        4.00        5.00      600.00        7.00        8.00
        5.00        6.00      700.00        8.00        9.00
***** balance matrix *****
        1.00        2.00       37.50        4.00        5.00
        2.00        3.00       50.00        5.00        6.00
       24.00       32.00        5.00       48.00       56.00
        4.00        5.00       75.00        7.00        8.00
        5.00        6.00       87.50        8.00        9.00
***** reduce to hessenberg form *****
    1.00e+00    3.94e+01    9.62e+00    3.33e+00    4.00e+00
    2.40e+01    2.73e+01    1.16e+02    4.80e+01    4.80e+01
    0.00e+00    8.55e+01   -4.78e+00   -1.33e+00   -2.00e+00
    0.00e+00    0.00e+00    5.19e+00    1.45e+00    2.17e+00
    0.00e+00    0.00e+00    0.00e+00    6.95e-08    4.77e-07