diff --git a/Direct Methods for Solving Linear Systems/Alg10.m b/Direct Methods for Solving Linear Systems/Alg10.m
new file mode 100644
index 0000000..44fb30b
--- /dev/null
+++ b/Direct Methods for Solving Linear Systems/Alg10.m	
@@ -0,0 +1,24 @@
+function A = Alg10(A)
+% Algorithm 10: Cholesky (Banachiewicz) factorization.
+% Matrix A has to be symmetric and positive-definite:
+% all d(i, i) > 0 for A = LDL^T.
+% We are using Outer product Version (Golub, Load, Alg. 4.2.2).
+
+[m, n] = size(A);
+
+if m ~= n
+    error('Matrix is not square!')
+end
+
+for k = 1:m
+   A(k,k) = sqrt(A(k,k));
+   A(k+1:n, k) = A(k+1:n, k)/A(k,k);
+   for j = k+1:n
+       A(j:n, j) = A(j:n, j) - A(j:n, k)*A(j, k);
+   end
+end
+
+A = tril(A);
+
+end
+
diff --git a/Direct Methods for Solving Linear Systems/Alg3_forward_substitution.m b/Direct Methods for Solving Linear Systems/Alg3_forward_substitution.m
index 472da08..a0618c0 100644
--- a/Direct Methods for Solving Linear Systems/Alg3_forward_substitution.m	
+++ b/Direct Methods for Solving Linear Systems/Alg3_forward_substitution.m	
@@ -3,7 +3,7 @@ function b = Alg3_forward_substitution(L, b)
 
     [m, n] = size(L);
     if m ~= n
-        error('Matrix is not squared!')
+        error('Matrix is not squar!')
     end
 
     if length(b) ~= m