Show that if (C, A) is detectable and (A, B) is stabilizable, then there exist matrices K and L

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Step 1: Understand the problem and definitions.
The problem asks us to show that there exist mat

Show that if $(C, A)$ is detectable and $(A, B)$ is stabilizable, then there exist matrices $K$ and $L$ such that $$ \sigma\left(\left[\begin{array}{cc} A & -B K \\ L C & A-B K-L C \end{array}\right]\right) \subset \Pi_{-} . $$