How do I get the solutions to this system of eqns

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

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

[Les Beckham]

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]

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.

Answer 1

[Sulaymon Eshkabilov]

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

Answer 2

[Sulaymon Eshkabilov]

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