Question

1. If A = 2 -1 म . find the general solution to 4 dx dt Ax

Answer 1

where A ( 4 ) and let xa d) Given system ax - Ax lis (²) Now find the eigenvalue of A. If & be an eigenvalue of a then, del (A-X1) 20 2-7 1 .ولا > 4-X 12 - 67 ag=0 23.3 et Na (2) be eigenvector of A 3. Then AU = 310 V 2 l John 23 4 N2

.. we get Ny + V2 (bz) -(0) This gives. Ve=2 ()-2) Particularly N221 gives, (1). How to find the solution of system (1) we need another veeton W = (W) such that, (A-31) W EV ربما لا راليا ( Jam)-(1) This gives - We + los ata W2 = 1+ Wy. wi دلها 30, wa W W, =0 1+wa) In particular gives. (6) so the general solution of (1) is, Steam libee (3)} [Where Cs, ce are arbi arbitrary constant] x= c et W + C2 034