$8\mathrm{.}4$ Find the state feedback gain for the state equation

x$($t$)=[112011001]$x$($t$)+[101]$u$($t$)\backslash$dot$\{$x$\}($t$)=\backslash$begin$\{$bmatrix$\}1$ & $1$ & $-2\backslash \backslash 0$ & $1$ & $1\backslash \backslash 0$ & $0$ & $1\backslash$end$\{$bmatrix$\}$ x$($t$)+\backslash$begin$\{$bmatrix$\}1\backslash \backslash 0\backslash \backslash 1\backslash$end$\{$bmatrix$\}$ u$($t$)$x$($t$)=100110211$x$($t$)+101$u$($t$)$

so that the resulting system has eigenvalues $2-22$ and $1$j$1-1\backslash$pm j$11$j$1.$ Use the method you think is the simplest by hand to carry out the design.