# 3 equations 4 unknowns

3 views (last 30 days)
Jens Petit-jean on 13 Dec 2020
Commented: Jens Petit-jean on 13 Dec 2020
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 on 13 Dec 2020
Edited: Cris LaPierre on 13 Dec 2020
Does a period (1.y) mean multiplication (1*y)?
Also, I see 4 unknowns (k, x, y, z).
Jens Petit-jean on 13 Dec 2020
yes the point means * sorry
and yes made a mistake I mean 4

Walter Roberson on 13 Dec 2020
%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 on 13 Dec 2020
thanks

Bruno Luong on 13 Dec 2020
Edited: Bruno Luong on 13 Dec 2020
>> 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