Math. 526 Numerical Linear Algebra Practice Test 1
February 08, 2010
Name
There are 6 problems. Show all work.
1. (15 points) Let v =
9
12
and w =
12
. Find:
9
(a) v + w
(b) The linear combination of v and w with coecients 2, 1.
(c) Compute the dot produc
Math 526 Practice Test 2
March 15, 2010
0 7 1
1 .
pr 1. (25 points) Let A = 3 1
15 9 9
(a) Find the L U P factorization of A.
(b) Use the L U Pfactorization of A to solve
x1
16
0 7 1
1
1 x2 = 11 .
3
15 9 9
x3
33
pr.2 (10 pts.) Let A be an nxm matrix, and
Math 526 Practice Test 3
April 13, 2010
2 6 4 4
pr.1 Let A be the matrix 10 30 20 6 .
8 24 16 8
(a) Find a basis for the subspace Null(A), Null(AT ), Col(A), Col(AT ); Find the
dimension of each of the four subspaces.
(b) Show that the subspaces Null(AT )
M ATH.
526
N UMERICAL L INEAR A LGEBRA P RACTICE F INAL E XAM
A PRIL
23, 2 010
Name:
T here are 8 problems in t his t est. Show all work.
1. (20 points) Let A
=
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3  2 10
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(a) F ind t he L  U factorization of A.
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~lATH 5 26 P RACTICE T EST 2
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pI" 1. (25 p oints) Let A =
3
is
15, 2 010
7 1]
.
1
9
1
9
(a) F ind t he L  U  P f actorization of A.
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Math 526 (Section 001 & 002), Fall 2015
Test 1
Name:
No books, notes, calculators, cell phones, PDAs, laptops, or any other aids allowed.
You must show all work as much as possible. Answers without work, even correct, will receive no credit.
Use the ba