Example 3. Given  .  Can A be factored  A = LU?    

Solution 3.

Use the LandU subroutine and see what happens.

We get a division by zero error, hence there is no LU-decomposition of A.

Remark.  The matrix A is nonsingular.  

We are done.  This shows that nonsingular is not sufficient to guarantee an  LU-decomposition.

Aside.  We can interchange rows and the new matrix B will have an   LU-decomposition.

(c) John H. Mathews 2004