Use matlab when programming.

$4$ Implementing Rotation Matrices

$4\mathrm{.}1$

Program the following functions. Here Rot$(x,)=$rotx$()$ means we rotate around the

$x-$axis by $$ radians.

$R=$rotx$()$

$R=$roty$()$

$R=$rotz$()$

$4\mathrm{.}2$

Multiply the following rotation matrices:

$R=$Rot$(z,\frac{}{4})Rot(y,-\frac{}{3})Rot(z,\frac{}{2})$

Prove that your answer $R$ is also a rotation matrix.

$4\mathrm{.}3$

Using $R$ from the previous part, show that $R^{-1}=R^T.$