218 CHAPTER 10. A FEW FACTORIZATIONS
10. Find the LU factorization of the coefficient matrix using Dolittle’s method and use itto solve the system of equations.
x+2y = 52x+3y = 6
11. Find the LU factorization of the coefficient matrix using Dolittle’s method and use itto solve the system of equations.
x+2y+ z = 1y+3z = 2
2x+3y = 6
12. Find the LU factorization of the coefficient matrix using Dolittle’s method and use itto solve the system of equations.
x+2y+3z = 52x+3y+ z = 6x− y+ z = 2
13. Find the LU factorization of the coefficient matrix using Dolittle’s method and use itto solve the system of equations.
x+2y+3z = 52x+3y+ z = 6
3x+5y+4z = 11
14. Is there only one LU factorization for a given matrix? Hint: Consider the equation(0 10 1
)=
(1 01 1
)(0 10 0
).
Look for all possible LU factorizations.
15. Find a PLU factorization of
1 2 11 2 22 1 1
.
16. Find a PLU factorization of
1 2 1 2 12 4 2 4 11 2 1 3 2
.
17. Find a PLU factorization of
1 2 11 2 22 4 13 2 1
.