I need to find the matching conditions for an adaptive system in terms of the $k_x$ and $k_r$ that satisfy:
$A+B K_x=A_m$
$B k_r=B_m$
Where: $A=\begin{pmatrix}-1 & 1\\1 & 0\end{pmatrix}$
$A_m=\begin{pmatrix}-1 & 1\\0 & -1\end{pmatrix}$
$B=\begin{pmatrix}0\\0.5 \end{pmatrix}$ $B_m=\begin{pmatrix}0\\1 \end{pmatrix}$
I obtained the value of the scalar $k_r$, which is 2, but I'm having issues with $K_x$. The equation is:
$B K_x=A_m-A$
$\begin{pmatrix}0\\0.5 \end{pmatrix}\begin{pmatrix}k_{x1} & k_{x2}\end{pmatrix}=\begin{pmatrix}0 & 0\\-1 & -1\end{pmatrix}$
How should I proceed? Maybe a pseudoinverse?