MATLAB Assignment 3.2: Parametric Vector Form My Solutions > Write a MATLAB function pvss that takes...

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MATLAB Assignment 3.2: Parametric Vector Form My Solutions > Write a MATLAB 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 in the following format: ▪ function [sscount, p, V] = pvss (A,b) ▪ sscount = -1 if the system is inconsistent (signaled by a pivot in the last column of rref ( [A b]). ▪ sscount = 0 if the system has a unique solution (signaled by a lack of free variables) ▪ sscount is the number of free variables of the system (number of columns of V) otherwise ▪p is the particular solution corresponding to all free variables being equal to zero (empty vector if sscount=-1), ▪ V is the matrix whose columns are homogeneous solutions (i.e. solutins of ) corresponding to one of the free variables equal to 1 while the others are 0 (empty list of columns if sscount <= 0). ▪ The provided template provides code to implement pvss except for the determination of v which can be implemented by completing four four lines in the code marked "UPDATE". Function > 1 function [sscount, p, V] = pvss(A,b) % For the linear system Ax=b finds the parametric vector form of the solution. 3 % If no solutions sscount=-1; otherwise, sscount is number of free variables 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 end % 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); r = size(pclist, 2); % CASE OF AN INCONSISTENT SYSTEM if r>0 && pclist (r)==n sscount = -1; p = zeros(n-1,0); V = zeros(n-1,0); return end % 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) % UPDATE: determine number of free variables (sscount) % UPDATE: find the list of free variables sscount = fvlist= v(pclist, :) = V(fvlist, :) = Save % rreduced row echelon form and pivot column list % number of pivot columns (rank(A)) % UPDATE: copy appropriately pivot rows of V from R % UPDATE: set free rows of V appropriately C Reset MATLAB Documentation Code to call your function > 1A=[1 2 3; 4 5 6; 7 8 9] 2 b=[1; 1; 1] 3 [sscount, P, V] = pvss (A, b) C Reset MATLAB Assignment 3.2: Parametric Vector Form My Solutions > Write a MATLAB 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 in the following format: ▪ function [sscount, p, V] = pvss (A,b) ▪ sscount = -1 if the system is inconsistent (signaled by a pivot in the last column of rref ( [A b]). ▪ sscount = 0 if the system has a unique solution (signaled by a lack of free variables) ▪ sscount is the number of free variables of the system (number of columns of V) otherwise ▪p is the particular solution corresponding to all free variables being equal to zero (empty vector if sscount=-1), ▪ V is the matrix whose columns are homogeneous solutions (i.e. solutins of ) corresponding to one of the free variables equal to 1 while the others are 0 (empty list of columns if sscount <= 0). ▪ The provided template provides code to implement pvss except for the determination of v which can be implemented by completing four four lines in the code marked "UPDATE". Function > 1 function [sscount, p, V] = pvss(A,b) % For the linear system Ax=b finds the parametric vector form of the solution. 3 % If no solutions sscount=-1; otherwise, sscount is number of free variables 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 end % 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); r = size(pclist, 2); % CASE OF AN INCONSISTENT SYSTEM if r>0 && pclist (r)==n sscount = -1; p = zeros(n-1,0); V = zeros(n-1,0); return end % 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) % UPDATE: determine number of free variables (sscount) % UPDATE: find the list of free variables sscount = fvlist= v(pclist, :) = V(fvlist, :) = Save % rreduced row echelon form and pivot column list % number of pivot columns (rank(A)) % UPDATE: copy appropriately pivot rows of V from R % UPDATE: set free rows of V appropriately C Reset MATLAB Documentation Code to call your function > 1A=[1 2 3; 4 5 6; 7 8 9] 2 b=[1; 1; 1] 3 [sscount, P, V] = pvss (A, b) C Reset

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