There is this "trick" to solve linear equations in all kinds of GA books:
GAmphetamine(3, () => {
// --- Vektor Definitionen (Spalten) ---
const v0 = 2*1e1 + 5*1e2 + 3*1e3;
const v1 = 3*1e1 + 1*1e2 + 2*1e3;
const v2 = 4*1e1 + 6*1e2 + 1*1e3;
const target = 32*1e1 + 47*1e2 + 18*1e3;
// --- Nenner-Volumen berechnen ---
const vol = v0 ^ v1 ^ v2;
console.log("Volumen: ", vol);
// --- Lösungen berechnen (Zähler / Nenner) ---
// Variable 0
const num0 = target ^ v1 ^ v2;
const ans0 = num0 / vol;
console.log("num0: ", num0);
console.log("135/45", 135/45); // 3
console.log("Ergebnis Variable 0: ", ans0); // 3.000000072643161
// Variable 1
const num1 = v0 ^ target ^ v2;
const ans1 = num1 / vol;
console.log("Ergebnis Variable 1: ", ans1);
// Variable 2
const num2 = v0 ^ v1 ^ target;
const ans2 = num2 / vol;
console.log("Ergebnis Variable 2: ", ans2);
});
Result:
Ergebnis Variable 0: 3.000000072643161
Ergebnis Variable 1: 2.000000048428774
Ergebnis Variable 2: 5.000000121071935
Instead of calculating 3 it's calculating 3.000000072643161 because it goes through the entire inverse. But it's both just two trivectors with one number component anyway:
We should be able to just check if both element have length 1 and do "normal" division?

There is this "trick" to solve linear equations in all kinds of GA books:
Result:
Instead of calculating 3 it's calculating 3.000000072643161 because it goes through the entire inverse. But it's both just two trivectors with one number component anyway:
We should be able to just check if both element have length 1 and do "normal" division?