circuit linear equation
After examining a circuit full of resistors, you find that the voltage at 4 specified points is given by:
\[\displaylines{
3v_{1} + 2v_{2} + 3v_{3} + 10v_{4} = 4 \\
2v_{1} - 2v_{2} + 5v_{3} + 8v_{4} = 1 \\
3v_{1} + 3v_{2} + 4v_{3} + 9v_{4} = 3 \\
3v_{1} + 4v_{2} - 3v_{3} - 7v_{4} = 2 \\
}\]
Where \(v_{1} - v_{4}\) are voltages.
Find \(v_{1},v_{2},v_{3},v_{4}\).
local numluau = require("@numluau")
local A : numluau.ndArray<number> = numluau.array({
{3, 2, 3, 10},
{2,-2, 5, 8},
{3, 3, 4, 9},
{3, 4,-3, -7},
})
local C : numluau.ndArray<number> = numluau.array({4,1,3,2})
local voltages = numluau.linalg.solve(A, C)
print(string.format("voltage results: \nv₁ : %g \nv₂ : %g \nv₃ : %g \nv₄ : %g",voltages[1],voltages[2],voltages[3],voltages[4]))