## A (15,11) Hamming code is used with the Generator matrix: 0 1 0 0 1 0 1 1 0 OOOOHOOOOOO 0 • Encode the message [0,1,0,1,0,1,0,1,0,1,0] • Decode the message from the received sequence [0,1,1,0,0,0,0,0,0,1,0,1,0,0, 1]

EXPERT ANSWER

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# Advanced Math

## 1 -3 2 -6 If T is defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A-| 0 1-2 | and b-1-26 5-16 10 Find a single vector x whose image under T is b

## Vehicles begin to arrive at a park entrance at 7:45 A.M. at a constant rate of six per minute and at a constant rate of four vehicles per minute from 8 A.M. on. The park opens at 8:00 A.M. and the manager wants to set the departure rate so that the average delay per vehicle is no greater than 9 minutes ( measured from the time of the first arrival until the total queue clears). Assuming D/D/1 queuing, what is the minimum departure rate needed to acheive this?

EXPERT ANSWER 6 . Let the pre-image of (-6,-26,-2)T be x = (a,b,c)T where a,b, c are arbitrary real numbers. Then T(x) =Ax = (-6,-26,-2)T or, (a-3b+2c, b-2c, 5a-16b+10c)T = (-6,-26,-2)T . Hence, a-3b+2c = -6 …(1), b-2c = -26…(2) and 5a-16b+10c= 10…(3). The augmented matrix of the above linear system of equations is M (say)= 1 -3 2 -6 …

Vehicles begin to arrive at a park entrance at 7:45 A.M. at a constant rate of six per minute and at a constant rate of four vehicles per minute from 8 A.M. on. The park opens at 8:00 A.M. and the manager wants to set the departure rate so that the average delay per vehicle …