The answer to exercise marked [BB]can be found in the Back of the Book.
A certain stale proposes to determine the check digit a12of a 12-digit driver’s license number a1a2 … a12 by the rule
12a1 + 11a2 + 10a3 + … + 2a11 +a12 = 0 (mod 10).
(a) Express this test in the form w · a = 0 (mod 10) for vectors w and a.
(b) [BB] Does this test detect an error in a single digit?
(c) Does this test detect the error resulting from the transposition of consecutive digits?
(d) Does it detect transposition errors in general?
Explain your answers.
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