$($a$)$ Find point $p$ in the $x,y$ plane of Figure $1$ by hand. Be sure to show each step in

the matrix product. $($b$)$ Apply your equations in MATLAB to confirm the result. $($c$)$

If ${}_1,$ now at $30,$ is increased to $90,$ how must ${}_2,$ now at $-45,$ change so that $p$

lies on the $x$ axis at $p^{\text{'}}=(x^{\text{'}},0)?$ Give values for $x_1$ and ${}_2$ in degrees. Hint: draw a

picture and use your knowledge of geometry.

If you can code the solution to part $c$ and generate a drawing in MATLAB similar to

Figure $1$ with the correct position of the robot arm, you will receive extra credit!