[VA] SRC #007 - 2020 April 1st Ramblings

[Bernd Grubert]

Hi Valentin,
thanks for the interesting excursion.

(04-01-2020 06:52 PM)Valentin Albillo Wrote:        1) Solving a system of N plain-vanilla linear equations in N unknowns is dead easy with most HP calculators but as soon as you introduce some very minor changes things aren't that easy anymore. For instance I wonder what the solution is for this system:

       u  + [v] + {w} = 200.0
      {u} +  v  + [w] = 190.1
      [u] + {v} +  w  = 178.8

This is actually a linear equation system consisting of 6 equations:

[u] + [v] = 199
[v] + [w] = 189
[u] + [w] = 178
{u} + {w} = 1.0
{u} + {v} = 1.1
{v} + {w} = 0.8

with u = [u] + {u}, ... and so on.
The constant term on the right side has to been adjusted to give positive solutions for the {}s.

The left side of the equation system can be written as matrix for solving in a calculator:
[1 1 0 0 0 0]
[0 1 1 0 0 0]
[1 0 1 0 0 0]
[0 0 0 1 0 1]
[0 0 0 1 1 0]
[0 0 0 0 1 1]

The solution is [94, 105, 84, 0.65, 0.45, 0.35], which results in:
u = 94.65
v = 105.45
w = 84.35