Question

(1 point) In this problem you will solve the nonhomogeneous system -2 5 -et j' 4 3et A. Write a fundamental matrix for the associated homogeneous system B. Compute the inverse C. Multiply by gand integrate T'g dt %3D +c2 (Do not include c, and c2 in your answers). D. Give the solution to the system (Do not include c, and c2 in your answers).

Answer 1

A. The eigen values of w-efficient matrix are given by, 1-2-1 5 1 -5 4-2=0 > A-4) (1+2) +25 = 0 *-22-8+25 = 0 » ^"-2X+17 =0 > - 2 4- 68 ^2 - 2 =) * = 273 1741 for Xi= 144² the eigen vector is given by, Vi= y 1 where, 1-2-(1+41) 5 - 1-5 4-614421 | 2 2 = (-3-42)2 + 512=0 7 542 = (3+415 41 het 9,=5 - Y2 = 3+42 com 1+ 41). Aytetits n 57 el climate inimese tas] tisinut e 1 3+41 et | 5034 tesisin 4t 3 0348-4 sinat +410348 +3i sinut

et 5 osat 5 . t sin 4* + e .1 3 cos 4t - 4sin 4th 4cos4 t + 3 sinut i fundamental matrix [set osat Betsin44 setasok_netinin neesat asetine) 2 24 det y = 20e los 4t tise 2 . L . osht sinut -15e ios 4d sinut +200 sinut = 2012+ ( cos”ud tsin" ak) 20.24 tos 4 a +36 sinut 4 e sinqt- zê w348] And Adjoint y = 1 set cosut used sinet netwos42 + 3e sinut 4e trinud-zetoset se tsinud] 5etwosut Adjoiny i Tét (960344 +3 sim4k) -5ētsinet ] dety Véx(4 sima 4-380944) sé * cos44 e) yig treut (410544 +3 sin4A) et (4 ringt-360g44) -hed sinet] 5-et. 5ē#c054 + Set

- (4 w34&t 3 sin 4A) – 15 sinuat Bron 4d-4 sinut + 15 cosat - 4 054ta 18 sinut 1 18 osut - 4 sinut 1 5.4 osat - 18 sin 4t dt I 18 cos 4t - 4 sinut => lo lg dt = 1/60 (- sinut + q cosat q sinut & osat

D' The solution to the system és, ý sveter swsgt 1 ssin4k + Ge 4cosyl 43sinut 1 3 00544 - 4 sin 4t + 4 felg det set sinad Tq Losad- sinat Now +144194 = + Set coset 1 et 1860842-4 sin4e) e (460544-3 since cos4x+q sinut = 545 (1054x+ sin4+) - 56034&sin4d+5 sin41054t 7 . 27 (654t-sin 4+)+4 (1054x+sin4x)=3sin44 60 541 - 18sing Aws 48+ issing to344-3sin44054* - 95 7 et 45 20 +4-3sinat Wet icosat +4 -6 sin 4t054t | Issinut at 55c034A 3.-.-F. ItGet . 4 cosut +3 sin 4+1 20 3 27 ws 8t -3 sin8t+41 344 - 45048