46. An unforced liner time invariant (LTI) system is represented by

\([{\dot x_1\over \dot x_2}] = \begin{bmatrix}-1&0\\0&-2\end{bmatrix} \begin{bmatrix}x_1\\x_2\end{bmatrix}\)

If the initial conditions are x1(0) = 1 and x2(0) = -1, the solution of the state equation is

(A) x1(t)= -1 , x2(t)=2

(B) x1(t)= -e-t , x2(t)=2e-t

(C) x1(t)= e-t , x2(t)= -e-2t

(D) x1(t)= -e-t , x2(t)= -2e-t


Answer-(C) x1(t)= e-t , x2(t)= -e-2t
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