# Matrix inversion and LU Decomposition. Having issues with the for loops and how they reference inputs.

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Susanna Westersund on 26 Oct 2020
Answered: Divija Aleti on 29 Oct 2020
function output =myMatrixInversion(A)
%% Problem Setup
i=1;
n=size(A);
AInv=zeros(n,n);
L=eye(n);
I=eye(n);
%% Forward Elimination w/ Multiplier Recording
% Reminder 1: Use nested loops
% Reminder 2: Use MATLAB vector/matrix operations wherever appropriate to replace unnecessary loops and simplify your code
% Reminder 3: Do not forget to display the updated coefficient matrix at the end of each FE step
for i=1:n-1 % run through each of the rows
for j=i+1:n % run through each of the columns
A(j,i+1:n)=A(j,i+1:n)-x*A(i,i+1:n)); % take the number and divide it
L(j,i)=A(j,i)/A(i,i); %simultaneously fill in L matrix
end
fprintf('\n\nIteration #%2d:\n', i)
fprintf(' The matrix is %.4e\n', A)
end
%% Forward Substitution
% Reminder 1: Use nested loops
% Reminder 2: Use MATLAB vector/matrix operations wherever appropriate to replace unnecessary loops and simplify your code
for i=1:1:n
sum=0;
for j=(i-1):1:n
sum=sum-L(i,j)*z(i,j);
end
z(i,j)=sum/L(i,i);
end
%% Backward Substitution
% Reminder 1: Use nested loops
% Reminder 2: Use MATLAB vector/matrix operations wherever appropriate to replace unnecessary loops and simplify your code
for a=1:n
for i=n:-1:1
sum=z(i,a);
for j=(i+1):1:n
sum=sum-U(i,j)*x(j,a);
end
x(i,j)=sum/U(i,i);
end
end
%% Final Output and Display
output=[L, U, z, x];
end
John D'Errico on 26 Oct 2020
What issues do you have? What exactly is your question?
Susanna Westersund on 26 Oct 2020
I'm struggling with my first set of nested for loops, and don't really know how to go about fixing the i and j values, like if I am referencing them right to create the upper and lower triangular matrix?

Divija Aleti on 29 Oct 2020
Hi Susanna,
I understand that you want to obtain the upper and lower triangular matrices and solve the equation 'Ax=I', to find the inverse of matrix 'A'. Do refer to the following links to get to know about the MATLAB functions that can be used to achieve this.