How do I get the solutions to this system of eqns

Question

Andrew 2023-10-17

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https://ww2.mathworks.cn/matlabcentral/answers/2034939-how-do-i-get-the-solutions-to-this-system-of-eqns

回答： Sulaymon Eshkabilov 2023-10-17

x = [ 1 1 1; -3 3+5i 3-5i; 9 34+30i 34-30i];

y = [28/3;15/2;9];

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Les Beckham 2023-10-17

在 MATLAB Online 中打开

x = [ 1 1 1; -3 3+5i 3-5i; 9 34+30i 34-30i]
x = 
   1.0000 + 0.0000i   1.0000 + 0.0000i   1.0000 + 0.0000i
  -3.0000 + 0.0000i   3.0000 + 5.0000i   3.0000 - 5.0000i
   9.0000 + 0.0000i  34.0000 +30.0000i  34.0000 -30.0000i
y = [28/3;15/2;9]
y = 3×1
    9.3333
    7.5000
    9.0000

That is not a system of equations, it is two assignment statements that create a complex matrix and a real column vector. Please specify the actual equation that you wish to solve.

Andrew 2023-10-17

x + y + z = 28/3

-3x + (3+5i)y + (3-5i)z = 15/2

9x + (34+30i)y + (34-30i)z = 9

this is the system.

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Answer 1

Sulaymon Eshkabilov 2023-10-17

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https://ww2.mathworks.cn/matlabcentral/answers/2034939-how-do-i-get-the-solutions-to-this-system-of-eqns#answer_1335099

在 MATLAB Online 中打开

Simply use \, linsolve(), inv(), etc. E.g.:

x = [ 1 1 1; -3 3+5i 3-5i; 9 34+30i 34-30i];
y = [28/3;15/2;9];
Solution1 = linsolve(x,y)
Solution1 = 
 -16.8485 + 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i
Solution2 = x\y
Solution2 = 
 -16.8485 + 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i
Solution3 = inv(x)*
Solution3 = 
 -16.8485 + 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i

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Answer 2

Sulaymon Eshkabilov 2023-10-17

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https://ww2.mathworks.cn/matlabcentral/answers/2034939-how-do-i-get-the-solutions-to-this-system-of-eqns#answer_1335109

在 MATLAB Online 中打开

You may also try lsqr(), rref(), svd(), and solve() with syms. E.g.:

x = [ 1 1 1; -3 3+5i 3-5i; 9 34+30i 34-30i];
y = [28/3;15/2;9];
Solution4 = lsqr(x,y)
lsqr converged at iteration 3 to a solution with relative residual 3e-10.
Solution4 = 
 -16.8485 + 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i
Sol = rref([x,y]);
Solution5 = Sol(:,end)
Solution5 = 
 -16.8485 + 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i
% svd()
[U,S,V]=svd(x);
Solution6 = V*inv(S)*U'*y
Solution6 = 
 -16.8485 - 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i
% solve() with syms --> NOT recommended though
syms x y z
A = [ 1 1 1; -3 3+5i 3-5i; 9 34+30i 34-30i];
b = [28/3;15/2;9];
Eqn = A*[x;y;z]==b;
Sol = solve(Eqn)
Sol = struct with fields:
    x: -556/33
    y: 144/11 + 535i/44
    z: 144/11 - 535i/44
Solution7 = double([Sol.x; Sol.y; Sol.z]) 
Solution7 = 
 -16.8485 + 0.0000i
  13.0909 +12.1591i
  13.0909 -12.1591i