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

[Albert Chan]

(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

Add them all, and halved it, u+v+w = 568.9/2 = 284.45 → {u}+{v}+{w} = .45, 1.45, 2.45
Assume {w}=0, eqn1 → {u}=0, eqn2 → {v}=.1, sum of fractional part does not match any of above.

Thus, eqn1 → {u}+{w} = 1 → {v} = 1.45-1 = .45
→ {u} = {190.1 - .45} = .65
→ {w} = 1 - {u} = .35

Removing all [], {}:

u + v = 200.0 + {v} - {w} = 200.1
v + w = 190.1 - {u} + {w} = 189.8
u + w = 178.8 + {u} - {v} = 179.0

→ (u, v, w) = (u+v+w) - (v+w, u+w, u+v) = 284.45 - (189.8, 179.0, 200.1) = (94.65, 105.45, 84.35)