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Lecture 31

# MATH 240 Lecture Notes - Lecture 31: Row Echelon Form, Gaussian Elimination, QiExam

Department
Mathematics
Course Code
MATH 240
Professor
Michael Monagan
Lecture
31

This 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, t2t, 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 P1P2, P2P3, P3
P1,P3P4, P1P4and P4P2. 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 QI4. If
you row reduce QI4to 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
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