Résolution de 4 équations à 4 inconnues :

* a +
* b +
* c +
* d =
* a +
* b +
* c +
* d =
* a +
* b +
* c +
* d =
* a +
* b +
* c +
* d =
a =
b =
Det =
c =
d =
(Remplir les cases grises)

d_ = a1*b2*c3*d4 - a1*b2*d3*c4 + a1*c2*d3*b4 - a1*c2*b3*d4
+ a1*d2*b3*c4 - a1*d2*c3*b4 - b1*c2*d3*a4 + b1*c2*a3*d4
- b1*d2*a3*c4 + b1*d2*c3*a4 - b1*a2*c3*d4 + b1*a2*d3*c4
+ c1*d2*a3*b4 - c1*d2*b3*a4 + c1*a2*b3*d4 - c1*a2*d3*b4
+ c1*b2*d3*a4 - c1*b2*a3*d4 - d1*a2*b3*c4 + d1*a2*c3*b4
- d1*b2*c3*a4 + d1*b2*a3*c4 - d1*c2*a3*b4 + d1*c2*b3*a4

da = y1*b2*c3*d4 - y1*b2*d3*c4 + y1*c2*d3*b4 - y1*c2*b3*d4
+ y1*d2*b3*c4 - y1*d2*c3*b4 - b1*c2*d3*y4 + b1*c2*y3*d4
- b1*d2*y3*c4 + b1*d2*c3*y4 - b1*y2*c3*d4 + b1*y2*d3*c4
+ c1*d2*y3*b4 - c1*d2*b3*y4 + c1*y2*b3*d4 - c1*y2*d3*b4
+ c1*b2*d3*y4 - c1*b2*y3*d4 - d1*y2*b3*c4 + d1*y2*c3*b4
- d1*b2*c3*y4 + d1*b2*y3*c4 - d1*c2*y3*b4 + d1*c2*b3*y4

db = a1*y2*c3*d4 - a1*y2*d3*c4 + a1*c2*d3*y4 - a1*c2*y3*d4
+ a1*d2*y3*c4 - a1*d2*c3*y4 - y1*c2*d3*a4 + y1*c2*a3*d4
- y1*d2*a3*c4 + y1*d2*c3*a4 - y1*a2*c3*d4 + y1*a2*d3*c4
+ c1*d2*a3*y4 - c1*d2*y3*a4 + c1*a2*y3*d4 - c1*a2*d3*y4
+ c1*y2*d3*a4 - c1*y2*a3*d4 - d1*a2*y3*c4 + d1*a2*c3*y4
- d1*y2*c3*a4 + d1*y2*a3*c4 - d1*c2*a3*y4 + d1*c2*y3*a4

dc = a1*b2*y3*d4 - a1*b2*d3*y4 + a1*y2*d3*b4 - a1*y2*b3*d4
+ a1*d2*b3*y4 - a1*d2*y3*b4 - b1*y2*d3*a4 + b1*y2*a3*d4
- b1*d2*a3*y4 + b1*d2*y3*a4 - b1*a2*y3*d4 + b1*a2*d3*y4
+ y1*d2*a3*b4 - y1*d2*b3*a4 + y1*a2*b3*d4 - y1*a2*d3*b4
+ y1*b2*d3*a4 - y1*b2*a3*d4 - d1*a2*b3*y4 + d1*a2*y3*b4
- d1*b2*y3*a4 + d1*b2*a3*y4 - d1*y2*a3*b4 + d1*y2*b3*a4

dd = a1*b2*c3*y4 - a1*b2*y3*c4 + a1*c2*y3*b4 - a1*c2*b3*y4
+ a1*y2*b3*c4 - a1*y2*c3*b4 - b1*c2*y3*a4 + b1*c2*a3*y4
- b1*y2*a3*c4 + b1*y2*c3*a4 - b1*a2*c3*y4 + b1*a2*y3*c4
+ c1*y2*a3*b4 - c1*y2*b3*a4 + c1*a2*b3*y4 - c1*a2*y3*b4
+ c1*b2*y3*a4 - c1*b2*a3*y4 - y1*a2*b3*c4 + y1*a2*c3*b4
- y1*b2*c3*a4 + y1*b2*a3*c4 - y1*c2*a3*b4 + y1*c2*b3*a4

Voir aussi Evaluating 4 x 4 Determinants by Recursion

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