10.9. EXERCISES 217

10.9 Exercises

1. Find an LU factorization of

 1 2 02 1 31 2 3

 .

2. Find an LU factorization of

 1 2 3 21 3 2 15 0 1 3

 .

3. Find an LU factorization of the matrix

 1 −2 −5 0−2 5 11 33 −6 −15 1

 .

4. Find an LU factorization of the matrix

 1 −1 −3 −1−1 2 4 32 −3 −7 −3

 .

5. Find an LU factorization of the matrix

 1 −3 −4 −3−3 10 10 101 −6 2 −5

 .

6. Find an LU factorization of the matrix

 1 3 1 −13 10 8 −12 5 −3 −3

 .

7. Find an LU factorization of the matrix

3 −2 19 −8 6−6 2 23 2 −7

 .

8. Find an LU factorization of the matrix

−3 −1 39 9 −123 19 −16

12 40 −26

 .

9. Find an LU factorization of the matrix

−1 −3 −11 3 03 9 04 12 16

 .