Chapter 4.5, Problem 7E

(a)

To determine

The rule $a_1+a_2+\mathrm{..........}+a_{10}\equiv 0\left(\mathrm{mod}11\right)$ in the form $\text{w}\text{.}\text{a}\equiv 0\left(\mathrm{mod}11\right)$ for some vectors w and a.

(b)

To determine

To prove: That the rule $a_1+a_2+\mathrm{..........}+a_{10}\equiv 0\left(\mathrm{mod}11\right)$ detects an error in a single digit.

(c)

To determine

To prove: That the rule $a_1+a_2+\mathrm{..........}+a_{10}\equiv 0\left(\mathrm{mod}11\right)$ does not detect a transposition of two (different) digits.