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4 appVersion 0.98.6179.21440 ≡

Solving matrix by the convention U^-1*V

local definition mode

Plug this algo in utilities,
collapsed top document. U V Msolve sols U 1 -^V * : 11 line :

# # 21 line

1. type ] 2. zap extra place holder ... click-on backspace

u 12 - 12 - 41 - 011 - 33 mat :

v 4 - 23 - 31 mat :

solutions are in ...
lexicographic order. X Y Z 31 mat u v Msolve : 16 - 9 - 6 - 31 mat

x...► y...► z...►

x ▼ y ▼ z ▼

by convention ► 1 x * 2 y * - 1 z * 2 x * - 4 y * 1 z * - 0 x * 1 y * 1 z * - 33 mat

solutions are ...
in descending order x y z 31 mat

naturally, each row of the matrix Σums what you want in 'v'

sanity check u X Y Z 31 mat * 4.000000000000000 - 2.000000000000000 3.000000000000000 - 31 mat

name solutions
as you whish wrt
project suite. α β ε 31 mat u v Msolve : 16 - 9 - 6 - 31 mat

sanity check u α β ε 31 mat * 4.000000000000000 - 2.000000000000000 3.000000000000000 - 31 mat

... @ this point, bear in mind that non integer numbers have no exact representation, resulting in non exact solutions

u v Clear u 107 8.1 7.2 7.08 5.04 658 5.98 9.89 9 6.99 4.99 9 9.98 44 mat : v 3223333141 mat : 13 mat 21 line

w x y z 41 mat u v Msolve : 80.9999999994497 - 136.99999999968 33.999999999936 - 21.9999999999771 41 mat

MCD 11 XP Pro.
recovers 10 D.
Smath Win 7
recovers 8 D u w x y z 41 mat * 32.0000000036164 23.0000000025528 33.0000000029155 31.0000000025971 41 mat

Wy not exact ? Answer: fractional numbers have no exact representation.

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u v Clear u 241122 mat : v 943521 mat : 13 mat 21 line

x y 21 mat u v Msolve : 231221 mat

u x y 21 mat * 94.000000000000000 35.000000000000000 21 mat