CHEE 3334
Fall ’97
Michael Nikolaou
EXAM 1
Openbook, opennotes.
Total points 100.
Please, budget your time
!
Do NOT try to read the book during the
exam!
Write neatly!
Do NOT use your programmable calculator to find results you are asked to compute in a
certain wayafter all, the calculator may find the wrong answer or not all answers!
Show all work.
Return
this sheet with your exam
.
GOOD LUCK!
1.
You are given the matrix
=
9
8
7
6
5
4
3
2
1
A
(1)
(10 pts.)
(a)
Find an LU decomposition for
A
.
(10 pts.)
(b)
Show how the above factors
L
and
U
can be used in forward and backsubstitution, to solve the system
of equations
Ax
=
b
, where
T
b
]
6
3
0
[
=
(2)
(Show your work.
Do not merely give the solution of
Ax
=
b
.)
(10 pts.)
(c)
Use the results of part (a) to calculate the determinant of
A
. (Show your work.
Do not merely give the
value of the determinant of
A
.)
2.
You are given the system of equations
=
1
1
4
3
2
1
2
1
x
x
(3)
(10 pts.)
(a)
Perform one iteration of the GaussSeidel method with the initial guess
=
1
1
)
0
(
2
)
0
(
1
x
x
.
(4)
(10 pts.)
(b)
Will the GaussSeidel method applied to the above equation (3) have guaranteed convergence?
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 Fall '06
 nikolau
 pts, initial guess, 10 pts, Gauss–Seidel method, Jacobi method, Eqn

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