Consider the IVPdx/dt= [row 1 2 2 row 2 2 2]x x(0)=[column 6 3]a) Find the

Question

-2]x x(0)=[column: 6 3]

a) Find the

eigenvalues and eigen vectors for the coefficient matrix

b) Find the solution to the IVP, give in real form: x(t)= [?]

X
12 :2 X ( + )
X . = (5 )
Jet ( A- XI ) = Jet ( ( 2 -2) – (0 2 ) )
= det ( ( – 2- 2 -2 ) )
= (-2-2) (-2-1) – (2) (-2)
= 4+41+12 + 4
= 16+ 4x+ 8
de : – 4+ 16- 32
2
s -2+ 2.
* = -2+2i
2 = – 2 – 2i…
Math