Question

1- Using clay Hamilton theory find eAt a) A- 21 b) A 1 0

Answer 1

A = [0 2 1 - 1] we have to find eigen values [XI - A] = [lambda 0 0 lambda] - [0 2 1 - 1] = [lambda -2 -1 lambda + 1]Vertical-bar lambda I - A Vertical-bar = lambda^2 + lambda - 2 = 0 by solving this lambda_1 = 1 lambda_1 = -2 therefore lambda = 1 & - 2 are eigen values consider m (lambda) = a_0 +_1 lambda (1 degree less than the circuit of A, order of a = 2) f(A) = e^^At f(lambda) = e^lambda t f(lambda) & m(lambda) must same values at lambda = 1, - 2 for lambda = 1 m (1) = a_0 + a_1 = f(a) implies a_0 + a_1 = e^t - (1) for lambda = -2 m (- 2) = a_0 - 2a_1 = f(- 2) = a_0 - 2a_1 = e^- 2t - (2) \r\n by solving equation (1) & (2)