$($Show work and steps. Circle$/$box final answers$)$ Problem $3$:

Given the following lateral$-$directional data for a jet aircraft:

C$\_($L$\_(0))=0,$C$\_($L$\_(\backslash$beta $))=-(0\mathrm{.}0822)/($r$)$ad$,$C$\_($L$\_(\backslash$delta a$))=(0\mathrm{.}1788)/($r$)$ad$,$C$\_($L$\_(\backslash$delta r$))=(0\mathrm{.}0150)/($r$)$ad

C$\_($N$\_(0))=0,$C$\_($N$\_(\backslash$beta $))=(0\mathrm{.}1095)/($r$)$ad$,$C$\_($N$\_(\backslash$delta a$))=-(0\mathrm{.}0760)/($r$)$ad$,$C$\_($N$\_(\backslash$delta r$))=-(0\mathrm{.}0365)/($r$)$ad

where

Y : side$-$force

$\backslash$beta : side$-$slip angle

L : rolling moment

N : yawing moment

$\backslash$delta a : aileron deflection with limits

$-25\backslash$deg $,+25\backslash$deg

$\backslash$delta r : rudder deflection with limits

$-20\backslash$deg $,+20\backslash$deg

a$30$ points$+5$ degrees of side$-$slip angle at trim. Do the required aileron and rudder deflections satisfy

or violate the given deflection limits$?$ Clearly explain your answer.

Note: If you need to solve a system of linear algebraic equations, you may use a calculator.