Question

Discrete Math 1: Please explain and prove each step with clear handwriting, and write every detail so that I can understand for future problems. This is discrete math one so please do not make it very complicated.

PLEASE MAKE THE HANDWRITING AND THE STEPS CLEAR AND ORGANIZED

Problem 2 (4 pts.): Solve the following recurrence relations together with the initial conditions. (a): an-2an-l + 3an-2 with ao = 2 and al = 4. (b): bn =-bn-l + 12bn-2 with bo = 3 and b1 = 2. Problem 3 (4 pts.): Write a recurrence relation together with the initial conditions for the number of different messages that can be transmitted in exactly n microseconds using three different signals when one signal requires 1 microsecond and the other two require 2 microseconds (each for the transmission, and each signal (except the last) in the message is followed immediately by another signal. Next solve it

Answer 1

Solution:

For Problem Ca)- Solve te followlinq Yecurrence velations togetteti the inikial cond: lions 1-2 wle have te chavactevistic Equation as 2 Hence,

herefore 2. and bi- 2 Similar ( 30,

For Problem 3: Wvite a recuence relation toqethey utt e na cond tions fort f drpperent Message ttat Can be Mt croseconds usind te different 5iqnals nitia tan 5mitted in xacle H eve fco)-1 c no Signal fc')-Kenly tte-Ast sgnal can be present at tte end oe econd lou can also vieus tis as 오 Signals stating 2 ticroseconds -second Signal, OY before) e ule can eve ite a closed -for fo tte Eqsuabon as we have e abix nukplrcation e determinant on fA λ-A-2-o Th - ' hich ay be -factored as CA-兆사) Thuś

Solvinq foY cand d, uhen, n- , Thus, tte clośed soluion is 23 +1 lhen, 8133 3 This Easc,5o e have veiHied ke solukon Ca), 50 le have vere