Homework 3

# Homework 3 - entries are positive.) 6. Exercises 2.4,...

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Homework 3 (Assigned: Sept 27, Due: Oct 6 (Wednesday)) 1. Exercises 2.2, Problem 30b, e (Hint: Express each row in RA as a linear combination of rows in A) 2. Exercises 2.3, Problem 1a 3. Exercises 2.3, Problem 3a 4. Consider Hamming code discussed in Example 4 (Section 2.3) (a) If the 4 bit data vector is b = [1, 1, 0, 0], what will be the coded 7 bit message c = [c 1 , c 2 , c 3 , c 4 , c 5 , c 6 , c 7 ]? (b) Let the received message be c’ = [0 0 1 1 1 1 0]. Assuming that there is at most one bit error during transmission, find the 7 bit message originally transmitted (i.e. c ) and the corresponding 4 bit data vector (i.e. b ). 5. Exercises 2.4, Problem 13 ( 1 is a vector containing all 1’s) (Hint: Observe that in any Markov transition matrix, the sum norm of each column = 1 and all the
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Unformatted text preview: entries are positive.) 6. Exercises 2.4, Problem 23 7. Exercises 2.4, Problem 34 8. . (a) Find and . (b) Let be any vector such that . Give an upper bound on . (i.e. find the maximum value of ). Find a vector with sum norm = 3 for which this bound is achieved. (i.e. Find a particular vector such that ). (c) Let be any vector such that . Give an upper bound on . Find a vector with max norm = 5 for which this bound is achieved. (Hint: To find the bounds, use the inequality ) 9. Exercises 2.5, Problem 16a, b...
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## This note was uploaded on 02/28/2011 for the course AMS 210 taught by Professor Fried during the Spring '08 term at SUNY Stony Brook.

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