Consider the system

\[\dot{\mathbf{x}}=\mathbf{A} \mathbf{x}\]

where \(\mathbf{A}\) is given by

\[\mathbf{A}=\left[\begin{array}{ccc}0 & 1 & 0 \\-b_{3} & 0 & 1 \\0 & -b_{2} & -b_{1}\end{array}ight]\]

(A is called the Schwarz matrix.) Show that the first column of the Routh's array of the characteristic equation \(\mid\) sI \(-\mathbf{A} \mid=0\) consists of \(1, b_{1}, b_{2}\), and \(b_{1} b_{3}\).