i want to solve a set of homogeneous linear equation

%Random example
A=magic(6);
n=size(A,1); 
syms x [n-1 1]
B=[1;x];
sol=solve(A*B==0,x)
sol = struct with fields:
    x1: 1
    x2: -1/2
    x3: -1
    x4: -1
    x5: 1/2

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Dyuman Joshi 2023-3-22

在 MATLAB Online 中打开

As I said earlier - "Note that you might not get a solution for x depending upon the values of A."

For the values you have for A, there is no solution for x.

P = 1.0e+04*[6.6064,-3.5642,0,0;-3.5642,6.6064,-3.5642,0;0,-3.5642,6.6064,-3.5642;0,0,-3.5642,3.2624];

na = size(P,1);

syms u [na-1 1]

Ba = [1; u];

%Let's solve for each equation corresponding to each row

y = P*Ba

y =

%1st equation, get the value of u1

U1 = solve(y(1)==0)

U1 =

%2nd equation, use u1 to get the value of u2

U2 = solve(subs(y(2),u1,U1)==0,u2)

U2 =

Now we have two equations remaining to get the value of u3, and the values of u1 and u2 will only be correct if we get the same u3 from

%value of u3 from 3rd equation

U3_1 = solve(subs(y(3),[u1 u2],[U1 U2])==0,u3)

U3_1 =

%value of u3 from 4th equation

U3_2 = solve(subs(y(4),u2,U2)==0,u3)

U3_2 =

As you can see, the values of u3 are not the same and hence there are no unique values for which the equation P*Ba=0 is satisfied.

The empty output (i.e. 0x1 sym) denote that there is no solution to the equation.

Shardul 2023-3-23

OK, Thanks for your help.

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Answer 2

Torsten 2023-3-23

0
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https://ww2.mathworks.cn/matlabcentral/answers/1933130-i-want-to-solve-a-set-of-homogeneous-linear-equation#answer_1199380

编辑：Torsten 2023-3-23

在 MATLAB Online 中打开

Or use the following code to produce an optimal solution in the least-squares sense:

A =1.0e+04*[6.6064,-3.5642,0,0;-3.5642,6.6064,-3.5642,0;0,-3.5642,6.6064,-3.5642;0,0,-3.5642,3.2624]
A = 4×4
       66064      -35642           0           0
      -35642       66064      -35642           0
           0      -35642       66064      -35642
           0           0      -35642       32624
C = -A(:,1);
B = A(:,2:end)\C
B = 3×1
    1.8535
    2.4356
    2.6609
A*[1;B]
ans = 4×1
    0.2555
    0.4735
    0.6221
    0.6797