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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem

Passports contain identification codes of the following form.

passport number check digit birth date check digit date of expiry check digit 012345678 4 USA 480517 7 F 020721 2 < < < < < < < < < < < < < final check 8

Each of the first three check digits is computed on the preceding identification numbers by using a weighting vector of the form

( 7 , 3 , 1 , 7 , 3 , 1 , ) in conjunction with congruence modulo 10 . For example, in this passport identification code, the check digit 4 checks the passport number, the check digit 7 checks the birth date, and the check digit 2 checks the date of expiry. The final check digit is then computed by using the same type of weighting vector with all the digits (including check digits, excluding letters). Verify that this passport identification code is valid.

0987654326USA1512269F9901018 < < < < < < < < < < < < < < < 4

0444555331USA4609205M0409131 < < < < < < < < < < < < < < < 8

0123987457USA7803012M9711219 < < < < < < < < < < < < < < < 3

0246813570USA8301047F0312203 < < < < < < < < < < < < < < < 6

(a)

To determine

To prove: The passport identification code is valid. Then, check the validity of the following passport identification codes.

Explanation

Given information:

Passport contains identification codes of the following form:

passportcheckbirthcheckdateofcheckfinalnumberdigitdatedigitexpirydigitcheck0123456784USA4805177F0207212<<<<<<<<<<<<<<<8

Each of the first three check digits is computed on the preceding identification numbers by using a weighting vector is of the form (7,3,1,7,3,1,...)

The passport identification code is,

0987654326USA1512269F9901018<<<<<<<<<<<<<<4

Formula used:

The dot product (x1,x2,...,xn)(y1,y2,...,yn) of two ordered n-tuples(vectors) (x1,x2,...,xn) and (y1,y2,...,yn) is computed by (x1,x2,...,xn)(y1,y2,...,yn)=x1y1+x2y2+...+xnyn

Explanation:

A weighting vector is (7,3,1,7,3,1,...).

First, let us check whether the passport number is correct or not.

For that, we need to compute (0,9,8,7,6,5,4,3,2)(7,3,1,7,3,1,7,3,1)

(b)

To determine

To verify: The passport identification code is valid. Then, check the validity of the following passport identification codes.

(c)

To determine

To prove: The passport identification code is valid. Then, check the validity of the following passport identification codes.

(d)

To determine

To verify: The passport identification code is valid. Then, check the validity of the following passport identification codes.

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