A single$-$wheel chair cart $($unicycle$)$ moving on the plane with linear velocity v and angular velocity canbe modeled by the nonlinear systempx $=$ vcos, py $=$ vsin, $=,$where $($px$,$ py$)$ denote the Cartesian coordinates of the wheel and its orientation. Regard this as a systemwith input u $=$ v T$($a$)(3$ points$)$ Construct a state$-$space model for this system with statex $=$x$1($t$)$x$2($t$)$x$3($t$)=$pxcos $+($py $1)$sinpxsin $+($py $1)$cosand output y $=$ x$1$ x$2$T $.($b$)(3$ points$)$ Compute a linearization for this system around the equilibrium point xeq $=0,$ ueq $=0.$