% Problem 1: % The A matrix is a 20 by 10 matrix with condition number 1.e1, % A is stored by row-wise, i.e. the first row, % the second row, ...., the 20th row. % 0.000000e+000 0.000000e+000 7.742637e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 9.443252e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 5.994843e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.291550e-001 0.000000e+000 0.000000e+000 0.000000e+000 1.668101e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.782559e-002 5.994843e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.154435e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 3.593814e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.782559e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 4.641589e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.291550e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 7.742637e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 7.742637e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 8.483821e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 4.641589e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.668101e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 3.593814e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.154435e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 % % b vector % 3.442749e-001 6.762369e-001 -9.607210e-001 3.625543e-001 -2.410380e-001 6.635920e-001 5.625768e-003 4.189428e-001 -1.422153e-001 -3.907653e-001 -6.206925e-001 -6.131377e-001 3.644464e-001 -3.944712e-001 8.334771e-002 -6.982540e-001 3.957970e-001 -2.432540e-001 7.200232e-001 7.073103e-001 % Problem 2: % The A matrix is a 20 by 10 matrix with condition number 1.e2, % A is stored by row-wise, i.e. the first row, % the second row, ...., the 20th row. % 0.000000e+000 0.000000e+000 5.994843e-005 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 9.443252e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 3.593814e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.668101e-002 0.000000e+000 0.000000e+000 0.000000e+000 2.782559e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 7.742637e-004 3.593814e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 4.641589e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.291550e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 7.742637e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.154435e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.668101e-004 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 5.994843e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 5.994843e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 8.483821e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.154435e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e-004 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.782559e-004 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.291550e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 4.641589e-004 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 % % b vector % 3.442749e-001 6.762369e-001 -9.607210e-001 3.625543e-001 -2.410380e-001 6.635920e-001 5.625768e-003 4.189428e-001 -1.422153e-001 -3.907653e-001 -6.206925e-001 -6.131377e-001 3.644464e-001 -3.944712e-001 8.334771e-002 -6.982540e-001 3.957970e-001 -2.432540e-001 7.200232e-001 7.073103e-001 % Problem 3: % The A matrix is a 20 by 10 matrix with condition number 1.e4, % A is stored by row-wise, i.e. the first row, % the second row, ...., the 20th row. % 0.000000e+000 0.000000e+000 3.593814e-009 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 9.443252e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.291550e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.782559e-004 0.000000e+000 0.000000e+000 0.000000e+000 7.742637e-004 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 5.994843e-007 1.291550e-005 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.154435e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.668101e-006 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 5.994843e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e-004 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 4.641589e-006 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.782559e-008 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 3.593814e-005 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 3.593814e-001 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 8.483821e-003 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 4.641589e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.000000e-008 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 7.742637e-008 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 1.668101e-002 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 2.154435e-007 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 % % b vector % .442749e-001 6.762369e-001 -9.607210e-001 3.625543e-001 -2.410380e-001 6.635920e-001 5.625768e-003 4.189428e-001 -1.422153e-001 -3.907653e-001 -6.206925e-001 -6.131377e-001 3.644464e-001 -3.944712e-001 8.334771e-002 -6.982540e-001 3.957970e-001 -2.432540e-001 7.200232e-001 7.073103e-001 % Problem 4: % The A matrix is a 20 by 10 matrix with condition number 1.e8, % A is stored by row-wise, i.e. the first row, % the second row, ...., the 20th row. % 0.000000e+00 0.000000e+00 1.291550e-17 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 9.443252e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.668101e-02 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.742637e-08 0.000000e+00 0.000000e+00 0.000000e+00 5.994843e-07 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.593814e-13 1.668101e-10 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.641589e-06 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.782559e-12 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.593814e-05 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.154435e-11 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.742637e-16 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.291550e-09 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.291550e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 8.483821e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.154435e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e-16 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 5.994843e-15 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.782559e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.641589e-14 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 % % b vector % 3.442749e-01 6.762369e-01 -9.607210e-01 3.625543e-01 -2.410380e-01 6.635920e-01 5.625768e-03 4.189428e-01 -1.422153e-01 -3.907653e-01 -6.206925e-01 -6.131377e-01 3.644464e-01 -3.944712e-01 8.334771e-02 -6.982540e-01 3.957970e-01 -2.432540e-01 7.200232e-01 7.073103e-01