# 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
##### 2 CommentsShowHide 1 older comment
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.