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+//Example 3.5

+clc

+clear

+

+A = [5 -2 1; 7 1 -5; 3 7 4];

+B = [4; 8; 10];

+

+n = length (B);

+L = zeros(n,n);         // L = Lower Triangular Matrix Initiation

+U = eye(n,n);           // U = Upper Triangular Matrix Initiation

+

+// LU Decomposition

+for i = 1:n

+    sum1 = zeros(n-i+1,1);

+    for k = 1:i-1

+        sum1 = sum1 + L(i:n,k) * U(k,i);

+    end

+    L(i:n,i) = A(i:n,i) - sum1;

+

+    sum2 = zeros(1,n-i);

+    for k = 1:i-1

+        sum2 = sum2 + L(i,k) * U(k,i+1:n);

+    end

+    U(i,i+1:n) = (A(i,i+1:n) - sum2) / L(i,i);

+end

+

+// Forward Substitution

+D = ones(n,1);

+for i = 1:n

+    sum3 = 0;

+    for k = 1:i-1

+        sum3  = sum3 + L(i,k) * D(k);

+    end

+    D(i) = (B(i) - sum3) / L(i,i);

+end

+

+// Back Substitution

+x = ones(n,1);

+for i = n:-1:1

+    sum4 = 0;

+    for k = i+1:n

+        sum4 = sum4 + U(i,k) * x(k);

+    end

+    x(i) = D(i) - sum4;

+end

+

+disp(strcat(["x1 = ",string(x(1))]))

+disp(strcat(["x2 = ",string(x(2))]))

+disp(strcat(["x3 = ",string(x(3))]))

+