Math 2270 Practice Final
-
University of Utah
Fall 2012
Name:
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7
This is a 2 hour exam. Please show all your work, as a worked problem
is required for full points, and partial credit may be rewarded for some
work in the right direction.
1
1. Elimination and LUFactorization
(a) Use elimination to calculate the row-echelon form of the matrix
i 2 0
(371)
5 2
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2.
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(b) (15 points) Calculate the LU factorization of the matrix from part
(a)
(1 20
(371
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/(371)
L C
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(c) (5 points) Is the matrix A positive-definite? How do you know?
Ij
A
b
3
2. (a) What is the rank of the matrix?
2314
2435
2556
0363
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6. What are the possible Jordan canonical forms for a 5 x 5 matrix with
eigenvalues A = 1, 1, 1,2,2.
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7. Is the transformation T(vi, v
)
2
Why or why not?
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=
0 ooa/
v a linear transformation?
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v
+
1
/
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3
10
8. (a) What is the incidence matrix for the graph:
00
H
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o
I
.
0
O
0
QO
11
(b) Perform elimination on the indicence matrix from part (a).
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/0
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ooQJ
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(c) What is the spanning tree for the graph from part (a) determined
by the reduction of the indicence matrix calculated in part (b)?
12