Unformatted text preview: ASE 311 Engineering computation, Fall 2009, Homework 5
Due: Friday, October 9, 2:00 PM in the lecture room JGB 2.216
Report all work, including any mﬁles you have written. You may also ﬁnd the command diary
useful in recording your MATLAB session. Please write clearly and be sure to label for which problem
each solution is.
Please, staple Part I and Part II separately and make sure that your name is written on both parts.
Part I
1. For which values of is the linear system
[ 2 ][ ] [ ] 1 1
1
=
1 1 2
0
nonsingular? What is the unique solution then?
2. Solve the above system with MATLAB using Gauss elimination with and without pivoting when = 10−4 , 10−8 . Compare with the exact solution.
Part II
3. Show that there cannot exist an LU factorization
[[ [
0 1
11 12
11 0
=
=
0 22
1 1
21 22
Hint: Equate the (1,1)elements and deduce that either the ﬁrst row or the ﬁrst column in
[][ ] must be zero.
4. Compute the factorization of the matrix in the previous exercise using MATLAB and
command lu. What is the permutation matrix [ ] such that [ ][] = [][ ], where [] is a
lower triangular matrix and [ ] an upper triangular matrix?
5. Perform a Cholesky factorization of
⎡
8
⎣20
15 the following symmetric system
⎤⎡ ⎤ ⎡
⎤
20 15
1
50
80 50⎦ ⎣2 ⎦ = ⎣250⎦
50 60
100
3 using the MATLAB builtin function chol and determine the solution for the given righthandside vector. ...
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 Spring '08
 KRACZEK
 Determinant, Triangular matrix, lecture room JGB

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