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Homework Assignment #2
Math 67
UC Davis, Fall 2011
Homework due. Tuesday 10/11/11
at discussion section.
Reading material.
Read Sections 3.2–4.3 in the textbook (the proof of the Fundamental
Theorem of Algebra in section 3.1 is optional material).
Problems
1. In an earlier lecture we encountered the (nonlinear) system of equations
x
+
y
=
1
5
x
+ 2
y
=
zx
2
x
+ 8
y
=
zy
which came up in the application of the Google PageRank algorithm. In that example,
in order to solve for
x,y
we had to provide the value of
z
without explaining how it
was obtained. This problem provides that missing explanation.
(a) Show how the second and third equations in the system lead to a quadratic equa
tion whose two solutions are the possible values of
z
, by applying the criterion
in “proofwriting exercise” 1 of Chapter 1 in the textbook.
(b) For each of the two values of
z
obtained in part (a), solve the system for
x
and
y
,
and explain why only one of the solutions makes sense (in terms of the meaning
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This note was uploaded on 11/13/2011 for the course MATH 67 taught by Professor Schilling during the Fall '07 term at UC Davis.
 Fall '07
 Schilling
 Linear Algebra, Algebra

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