parametric vector form - matrix

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Seungryul Lee
Seungryul Lee 2022-10-1
评论： Dyuman Joshi 2022-10-2
Hi, I have a function pvss that takes as input the coefficient matrix and right hand side of a linear system and returns the parametric vector form of the solution.
And these are the formats:
And here is my code:
function [sscount, p, V] = pvss(A,b)
% For the linear system Ax=b finds the parametric vector form of the solution.
% If no solutions sscount=-1; otherwise, sscount is number of free variables
% p is the particular solution with the free variables equal to zero (empty if sscount== -1)
% ith column of V is the homogeneous solution corresponding to the ith free variable (empty if sscount <= 0)
Augmented = [A b];
[m, n] = size(Augmented);
[R, pclist] = rref(Augmented); % rreduced row echelon form and pivot column list
r = size(pclist,2); % number of pivot columns (rank(A))
% CASE OF AN INCONSISTENT SYSTEM
if r>0 && pclist(r)==n
sscount = -1;
p = zeros(n-1,0);
V = zeros(n-1,0);
else
sscount=n-r;
% OBTAIN THE PARTICULAR SOLUTION
p = zeros(n-1,1);
p(pclist) = R(1:r,n);
% OBTAIN THE HOMOGENEOUS SOLUTIONS CORRESPONDING TO EACH FREE VARIABLE (IF ANY)
V(pclist,:) = -R(1:r,n); % UPDATE: copy appropriately pivot rows of V from R
V(n,:) = eye(sscount);
end
% UPDATE: set free rows of V appropriately
end
And this is the code to call the function:
A=[1 2 3; 4 5 6; 7 8 9]
b=[1; 1; 1]
[sscount, p, V] = pvss(A,b)
I've tested with some cases, and I passed a few tests, but I'm keep getting an error for this example
How should I fix my code to get a correct output for all sizes of matrix?
  1 个评论
Dyuman Joshi
Dyuman Joshi 2022-10-2
You are assigning a matrix to a row (as stated in the error as well), which is not possible.
V(n,:) = eye(sscount)
What exactly do you want to perform with respect to this line of code?
In case of a particular solution, what is the expected size of V?

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