$(50$ point$)$ Assume that $a,b,c$ and $d$ are defined as follows:

$a=\left[\begin{array}{cc}2& 1\\ -1& 4\end{array}\right],b=\left[\begin{array}{cc}-1& 3\\ 0& 2\end{array}\right],c=\left[\begin{array}{c}2\\ 1\end{array}\right],d=$eyc$(2)$

Use MATLA to calculate the results of the following expressions if they are legal. If an

operation is illegal, explain why.

$a+b$

$a^{*}b$

a $.*$ d

a$*$c

a$.*$ c

$\frac{a}{\frac{?}{?}}b$

a$.\backslash$b

$a{*}^{{?}^{?}}b$

$-\frac{11}{5}$

$\frac{5}{\frac{?}{?}}-11$

round $(-\frac{11}{5})$

ceil$(-\frac{11}{5})$

floor$(-11/5)$

$(50$ points$)$ Position and Velocity of Ball If a stationary ball is released at a height $h_0$ above the

surface of the earth with a vertical velocity $v_0,$ the position and velocity of the ball as a function

of time will be given by the equations

$h(t)=\frac{1}{2}g{t}^2+v_{0}t+h_0$

$v(t)=gt+v_0$

Where $g$ is the acceleration due to gravity $(-9\mathrm{.}81\frac{m}{s^2}),h$ is the height above the surface of the

Earth $($assuming no air friction$),$ and $v$ is vertical component of velocity.

Write a MATLAB program that prompts a user for the initial height of the ball in meters

and the initial vertical velocity of the in meters per second.

Plot the height and vertical velocity as a function of time for the first $25$ seconds. Be sure

to include proper labels in your plots.