Question

Homework 10: Problem 9 Previous Problem Problem List Next Problem (1 point) Solve the following initial value problem: (2 -10 6 0 -10 8) x=10-25|又 dt 孔0)=12 Xi = x2

Answer 1

Let A = matrix 2 0 0 - 10 - 2 - 10 6 5 8 = let A be the co factor of for all 2 5 = 1 2 3 A_11 = -16 + 50 = 34 A_22 = 16 A_33 = -4 A_11 + A_22 + A_33 = 46 trace A = 8 det A = 2 (- 16 + 50) = 68 characteristic polynomial of a is delta = delta^3 + (trace A) Lambda^2 - (A_11 + A_22 + A_33) lambda + (det A) = lambda^3 + 8 lambda^2 - 46 lambda + 68 delta = 0 implies lambda^3 - 8 lambda^2 + 46 lambda - 68 = 0 (lambda -) (lambda^2 - 6 lambda + 34) = 0 therefore lambda = 2 lambda = 6 plusminus squareroot/2 = 6 plusminus 10/2 lambda = 2 and 3 plusminus 5 let v_1 = [a b c] is an eigenvector of A corresponding lambda = 2 then (A - 2I)