# 46. The state transition matrix φ(t) of a syst...

46. The state transition matrix φ(t) of a system $\begin{bmatrix}\dot x_1\\\dot x_2\end{bmatrix} = \begin{bmatrix}0&1\\0&0\end{bmatrix} \begin{bmatrix}x_1\\ x_2\end{bmatrix}$

(A) $\begin{bmatrix}t&1\\1&0\end{bmatrix}$

(B) $\begin{bmatrix}1&0\\t&1\end{bmatrix}$

(C) $\begin{bmatrix}0&1\\1&t\end{bmatrix}$

(D) $\begin{bmatrix}1&t\\0&1\end{bmatrix}$

Hint:
Explanation:

Answer-(D) $\begin{bmatrix}1&t\\0&1\end{bmatrix}$
Discuss the solution.