Millersville University
Department of Mathematics
MATH 375, Homework 6
November 6, 2003
The completed assignment is due at class time on Tuesday, 11/11/2003. You may use your
textbook, computer programs, and notes. All numerical approximations must be accurate
to within 10−4unless otherwise stated.
1. Consider the system of equations
14 14 −9 3 −5
14 52 −15 2 −32
−9−15 36 −5 16
3 2 −5 47 49
−5−32 16 49 79
x1
x2
x3
x4
x5
=
−15
−100
106
329
463
.
Find the LU factorization of A. Use forward- and backward-substitution to solve the
linear system.
2. A symmetric, positive definite matrix Acan be factored into the form A=LLtwhere
Lis a lower triangular matrix. Consider the matrix
9/4−3 9/2
−3 5 −10
9/2−10 34
,
let matrix Lhave the form
l11 0 0
l21 l22 0
l31 l32 l33
and find Lsuch that LLt=A. You do not have to verify that Ais positive definite.