3 equations 4 unknowns

hello,

How do you make a matrix M 3x3 so the system is =k.MX (with X a 3x1 matrix [x,y,z] I think.)

x=k.(1.y+6.z)

y=k.(4.x+4z)

z=k.(0.x+1.y)

[Cris LaPierre]

Does a period (1.y) mean multiplication (1*y)?

Also, I see 4 unknowns (k, x, y, z).

[Jens Petit-jean]

yes the point means * sorry

and yes made a mistake I mean 4

Answer 1

[Walter Roberson]

%x=k.(1.y+6.z)
%y=k.(4.x+4z)
%z=k.(0.x+1.y)

syms x y z k
X = [x; y; z];
eqn = X == k * [0 1 6; 4 0 4; 0 1 0] * X

eqn = 

sol = solve(eqn, [x, y, z])

sol = struct with fields:
    x: [1×1 sym]
    y: [1×1 sym]
    z: [1×1 sym]

sol.x

ans = 

0

sol.y

ans = 

0

sol.z

ans = 

0

[Jens Petit-jean]

thanks

Answer 2

[Bruno Luong]

>> M=[0 1 6; 4 0 4; 0 1 0];
>> [X,K]=eig(M);
>> k=1./diag(K);

% select 3rd eigen vector for example
>> X(:,3)

ans =

    0.5508
    0.8070
    0.2131

>> k(3)*M*X(:,3)

ans =

    0.5508
    0.8070
    0.2131