Consider the system below: $$ begin{array}{1} dot{x}_{1}=3 x_{1}-7 x_{2} dot{x}_{2}=alpha x_{1}+4 x_{2} end{array} $$ with...

 

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Consider the system below: $$ \begin{array}{1} \dot{x}_{1}=3 x_{1}-7 x_{2} \\ \dot{x}_{2}=\alpha x_{1}+4 x_{2} \end{array} $$ with output $$ y=\alpha x_{1}+3 x_{2} $$ where $\alpha$ is a costant. Find the values of $\alpha$ for which the system is completely observable. Consider the system below: $$ \begin{array}{1} \dot{x}_{1}=3 x_{1}-7 x_{2} \\ \dot{x}_{2}=\alpha x_{1}+4 x_{2} \end{array} $$ with output $$ y=\alpha x_{1}+3 x_{2} $$ where $\alpha$ is a costant. Find the values of $\alpha$ for which the system is completely observable.