7. (10 points) A routing transit number (RTN) is a bank code used in the United States which appears on the bottom of checks. The most common form of an RTN has nine digits, where the last digit is a check digit. If d1 d2... d9 is a valid RTN, the congruence 4(d1 +d4 + d7) + 3(d2 +d5 + d8) + (d3 + d6 + d9) = 0 (mod 10) must hold. a) (7 points) Show that if dl d2... d9 is a valid RTN, then d9 = 6(d1 + d4 + d7) + 7(d2 +d5+ d8) + 9(d3 + d6) mod 10. b) (3 points) Use (a) to find the check digit that follows the eight digits 11100002 in a valid RTN.