Question

(1 point) In this problem you will solve the nonhomogeneous system 3-(: +3]3+ [3] 3 -2 9-3 A. Write a fundamental matrix for the associated homogeneous system Y = B. Compute the inverse Y-1 =

Answer 1

Given :- 9 = 5-3 S one; Given :- gt [53]-[-] To ]+ :) -3 Sol". A 3 and og y. -er { consider the characteristic palynenial det (A-XI) -3-X -2 -0 a - 3-X --box; 2 A²-9 +18=0 A +9=0 - 31 - 31 -3! the Eigen values are d, 31, 12 : 80px; Pecs now center; y we have to find the Eigen vector for corresponding Eigen value far x=31 det (A-(31)I) 3.-31 -3-31 -2 Y, -0 > nderline; 42 5em 0; 9

33 3-31 -3-30 9 yn **) (3) 0 .. The eigen vedor core to d=3ė the Eq" foem is 9, + ( + 1/2 + 1 )% =0 39 = is 050-45-4) 86 9 ( 3.) 92 now we have to find eigen vector for the corresponding Eiges value x=-31 ♡ - + 3 (

3 sir (at) 12 cas (3+) - a sir (34) -3 cas (34) 9 cas 13+J+12331 (34) C) From 6 we have al home & to find vlg leidt net g Lt) +=(+ 12 cas3t - 984 34 3 sin 3t 89 (t) = a les 3t + 12 sist -3 ast - 12 sin3t - 12 cas 3t+9 sinst -12 51732 - 12 sasst - a cas3t - 12 si 37. -3 sin 37 12 cast -21 cas 3t - 12 sint Now Sy goodt St3ein 3t 12 cas3t)dt 21 cas37 -12 sin3tlat Stricas

5 D) general selation is ý Lt) = 3 cas (3 t) + 1 sinat cas 34 + ₂ I as 13t) + 3 / 2 sinat sin 3t u sint cas 34 7 7 sin 3t tu cas 34 conclusion :- All the parts solved