Question

For the matrix A, find real closed formulas for the trajectory$\overrightarrow{\mathbf{x}}\mathbf{(}\mathbf{t}\mathbf{+}\mathbf{1}\mathbf{)}\mathbf{=}\mathbf{A}\overline{\mathbf{x}}\mathbf{\left(}\mathbf{t}\mathbf{\right)}$where $\overrightarrow{\mathbf{x}}\mathbf{=}\left[\begin{array}{c}0\\ 1\end{array}\right]$. Draw a rough sketch

$\mathit{A}\mathbf{}\mathbf{=}\mathbf{}\left[\begin{array}{cc}1& 5\\ -2& 7\end{array}\right]$

Short answer

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously

Step-by-step solution

Define Trajectory

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously

Finding the trajectory

Solving the equation