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Lecture 31

School

Simon Fraser UniversityDepartment

MathematicsCourse Code

MATH 240Professor

Michael MonaganLecture

31This

**preview**shows half of the first page. to view the full**1 pages of the document.**MATH 240 Assignment 4, Fall 2018

Michael Monagan

Due 8pm Monday November 5th. Sorry, no late assignments are accepted.

We will (aim to) post the solutions at 8:30pm.

Test 3 is on Wednesday November 7th class.

4.4 Exercises 2, 6, 12, 14, 23, 24, 32(a)

For exercise 12 use instead the basis B={[5,3],[2,1]}which has a ”nice inverse”.

4.5 Exercises 2, 14, 19, 22.

Additional exercise: What is dim(S) where S=Span(1 + t, 1 + t2, t2−t, t3) in P3?

4.6 Exercises 2, 5, 6, 15, 16, 25

4.9 Exercises 3, 9, 10, 13, 17

Additional exercise for internet page ranking.

Suppose you have web pages P1, P2, P3and P4with hyperlinks P1→P2, P2→P3, P3→

P1,P3→P4, P1→P4and P4→P2. Assuming a web-surfer takes the hyperlinks on

a web page with equal probability, construct the 4 by 4 Markov matrix Q. Now solve

Qq =qfor the probability vector qsuch that q1+q2+q3+q4= 1. Hence determine

the ranking of the pages. You will need to row reduce the 4 by 4 matrix Q−I4. If

you row reduce Q−I4to reduced row echelon form you should get

1 0 0 −2/3

0 1 0 −4/3

0 0 1 −4/3

0 0 0 0

5.1 Exercises 1, 6, 10, 18, 21, 24, 27

1

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