Question

Question 1. Find a fundamental set of solutions of each of the following two-dimensional systems. 1 (i) x = X -3 1 ii) * = ['z 32 *

Answer 1

E *-[ :7* Eigen value of Ali o au gleen by | A-AI/=0 → 7=-1+1, -1-1 =(aj be the Vector Corres Eger het c 7= -1 ti o responding - /A-(-1+i) I/C=0 2-1 -5 O =) (2-1) G-56-o G+ G-x-e) so 3 goloving there for Equation ato C 1

Let D = d ] d be the Gigen Vector Corresponding value -1-1 to the Eigen [4-(4-2)2) = [A + (1+i) z] [b]= (0) 240 -S 1 ):)-6 } solve Ga (2+2)d, -sd, co di + oe (-2+i)=0 we get D - fundamental sel tila (2x & De oft Solution to use 178273 y (x)

hat D-d be the bigen Vector corresponding d to the Ergen Value A=0 - [A +22)D=0 13 [ 11.) CJ-45) ocx d, +3d₂=0 } Pole 5d, +35dco =) d, -3, dat 0-17) e lears)x and be two golation Then General Solution is 1+312) Y(x) = ac (+352) 9.C*) linearly Inolebende Apo e 4,6x) e J--[70] Please Rate w, Thank you