1
Math 410-001, Spring 2012: Test 1
Test 1
Math 410-001
Zhao
February 20, 2012
-~f_'):,_ _ CVVID: _ _~
NAME:
Instructions: There are 8 problems. The last problem is a 5-mark bonus. You may not
use you
Solutions to Selected Problems In:
Fundamentals of Matrix Computations: Second Edition
by David S. Watkins.
John L. Weatherwax
June 8, 2007
Chapter 1 (Gaussian Elimination and Its Variants)
Exercise 1
HW3 Solution of Math170A
Shi(Fox) Cheng
Feb 15th, 2012
4.1.6
Proof.
(i) It is not hard to see
AV = Av1
Av2
Avm
= 1 u1
r ur
0
0 = U ,
which is exactly the left half of equations (4.1.4), where ui and v
HW4 Solution of Math170A
Shi(Fox) Cheng
Feb 27th, 2012
5.3.6
(i) Find eigenvalues.
Consider
det(A I) = 2 11 + 17 = 0
Apply quadratic formula one can easily nd two roots 1 = 9.1401 and 2 = 1.8599.
(ii)
% Homework 7 computer problem
% Exercise, 4.2.8
format long
0ouble precision outputs
A = randn(3)
0efine a random square materix
A =
1.19083807424337
-1.20245711477394
-0.01978955776877
cond(A)
-0.156
1
Math 410-001, Spring 2012: Test 2
April 2, 2012
Test 2
Math 410-001
NAME: _.~.-<_e~;/:._ _
Zhao
CVVID: _
Instructions: There are 7 problems. The last problem is a 5-mark bonus. Show all work;
if you