Consider the discrete$-$time state$-$space equation

x$[$k $+1]=$

$$

$112$

$011$

$001$

$$

$$ x$[$k$]+$

$$

$1$

$0$

$1$

$$

$$ u$[$k$]$

y$[$k$]=200$ x$[$k$]$

Find the state$-$feedback gain so that the resulting system has all eigenvalues at z $=0.$ Show that for

any initial state, the zero$-$input response of the feedback system becomes identically zero for k $3$