Question

Find the general solution of following equation

x' = [ -3 sqrt(2)

sqrt(2) -2 ] *x

It's a matrix problem, so x' = [ ] x

Hopefully that makes sense, thanks in advance

Answer 1

Key paint : Let PLH) be the characteristic polynomial and P(A) = o has two distances n(t) = c velit of A, for a' (t) = Aalt), real soluations to and da. Let 6, and b = associate eigen vector (ie. Avi 7, 4, ; A U2 = 1202 ) then the general gsolution is var V22 are V21 - _ te q ezt Given V2 3 2 ] - 2 - A - -3 √2 and p (t) = x +50 + 4 = (2+1) (4+4). = 8 (2) 20 has two distinct real solnations -3-4 Ford=-1 Ald=10 0 :-) (A-XI) 6, = (A + I) 0,= 0 - 3+1 12 JCJ-L0] -2+1

N 0 9 1 ( / / / 2011.00 น L - 2 9. tN2 9 | 5 6 ! N) 9, V2 | - 92 - N) 9, 1) 9 1 - ง 9ม taking on WLC 9) 5 - For t= - 4 A - - 492 7 (A +AI ) 9, _ ๐ “าว ๆ มา 3 344 คน N- 91 -264 9. ) 1 21 ][ 12 ] 2-6 ๆ 92 + N, V, N, 9, +2.226 and | 912 ป, 92

มา -n 622 92 [ 3 - V22 [ v22 ger Taking 022=1 √2 102 [] ::alt) = e, c, o, edit + 22 et 26 t 2 il.nit) e

Where c_1,c₂ are arbitrary constants.

Hope it's helpful for you.!!

Thank you...