An ISBN Number

Suppose an operator types a US Bank Check Code into a machine and transposes two adjacent digits (i.e. swops the order of two adjacent digits) for example the operator types

a_{3} a_{2}

instead of

a_{2} a_{3}

, will the machine pick up every error of this type? Does the same apply to ISBN numbers, will a machine detect transposition errors in these numbers?

US bank check codes are nine digit identification numbers

a_{1} a_{2} \dots a_{9}

using the digits 0 to 9 where

7 a_{1} + 3 a_{2} + 9 a_{3} + 7 a_{4} + 3 a_{5} + 9 a_{6} + 7 a_{7} + 3 a_{8} \equiv a_{9}

mod 10.

ISBN Numbers have ten digits

a_{1} \dots a_{10}

using the digits 0 to 9 where

10 a_{1} + 9 a_{2} + 8 a_{3} + \dots + 3 a_{8} + 2 a_{9} + a_{10} \equiv 0 \mod 11 .