Solving homogeneous systems of linear equations

Hello everybody,

I was trying to solve a homogeneous system of linear equations by using the null() function, which is recommended by https://de.mathworks.com/help/matlab/math/systems-of-linear-equations.html. But I'm kind of stuck because the function always returns the Error "Empty sym: 1-by-0".

I already tried a more simple example, where the solution is already known.

Example =

[ 5529.6571965113201121628855218102,                             -3000]
[                             -3000, 1627.5873313951778400904919565612]

>> null(Example)

ans =

Empty sym: 1-by-0

It should return the vector x = [0.477; 0.879]. Or am I missing something?

Answer 1

[Torsten]

If I execute

    A=[ 5529.6571965113201121628855218102,-3000
        -3000, 1627.5873313951778400904919565612];
    null(A)

I get the correct result.

Best wishes

Torsten.

[Henan Fang]

Dear Torsten, can you tell me why my generated matrix like the example above (every line has a square bracket)? My codes are as follows.

clear all;
syms kz x y
x=0.5;
y=0;
m = 2;
vh = 4;
mu = 11;
delta = 8;
HBAR = 1.05457266e-34;
ME = 9.1093897e-31;
ELEC = 1.60217733e-19;
Kh = 2.106;
vKh = [0,0,0;Kh,0,0;-Kh,0,0;0,Kh,0;0,-Kh,0];
kc = sqrt(2*ME*ELEC/HBAR^2)*1e-10;
ku = kc*sqrt(mu+delta);
kd = kc*sqrt(mu-delta);
a3 = [pi/Kh,pi/Kh,sqrt(2)*pi/Kh];
kuu =@(x,y) [-ku*sin(x)*cos(y), -ku*sin(x)*sin(y), kz];
n=0:m;
for p=1:5;
    for q=1:5;
    tuu(p,q)=(sum((kuu(x,y) + vKh(p,:)).^2)-ku^2)*(p==q)+ kc^2*vh*sum(exp(i*n*sum((vKh(q,:)-vKh(p,:)).*a3)))*(p~=q);
    end
end
tuu