Important : Directly thumb down for copying other's answer on chegg. please do not copy since I have already read them

Use the matlab only and follow the steps given in the hints to solve this question. Give out your matlab code and explanation will be even better if you have them. Definitely Thumb up for helpful answers written by yourself and following the steps.

PROBLEM 3 There are many mathematical applications where we want to rotate objects about an axis in R3 (three- dimensional space). For example, when controlling an aircraft, rotations about different axes are known as yaw, pitch and roll. Imagine that an object is at position x = (x, y, z) (a column vector representing the x, y, and z coordinates). To rotate this vector counterclockwise by an angle about the y-axis, you can multiply x by the matrix cos 0 0 sine R(0) = 0 1 0 - sin 0 0 cos) In other words, b = R(@)x is the rotated vector of x. (1) Write a function that takes e as an argument and returns the matrix R(O). Use this function to calculate R(7/8) and save this matrix in a variable named A11. (2) Suppose we have the vector x = (1/10, 2.1, -e). Rotate this vector about the y-axis by an angle of 1A/3. Save the resulting 3 x 1 vector in a variable named A12. (3) Suppose that we have a vector b = (1.4, -1/10, 2.8) (a column vector), which was obtained by rotating another vector x about the y-axis by an angle of /6. Find the vector x by solving the appropriate 3 x 3 matrix equation. Save the resulting 3 x 1 vector in a variable named A13. (4) Find the inverse matrix of R(37/4) (using inv in MATLAB or scipy.linalg.inv in python). Save your answer in a variable named A14. (While we don't want to use inverse to solve matrix equations, there are times when we will need to just calculate the inverse.) (5) This is an application where inverse matrices are used quite often, but it is still a bad idea to actually use the inverse command. But can we figure out an easier way to do it? The inverse of a rotation is just another rotation. That is, R(0)-1 = R(), where o is a different angle. Find the angle o such that R(3/4)-! = R(). Save this answer in a variable named A15. (This does not require any code, just some geometric reasoning. If you rotate a vector by an angle e, what would you have to do to rotate the vector back to where it started? The answer is not unique, because adding any multiple of 27 to an angle gives the same rotation matrix. Your answer should be between -7 and 7.) %%% Problem 3 %%% First go to the end of the file to create your function %%% After you make your function come back to this line. %% Save A11 as R(pi/8) %%% Rotate the vector given in the assignment file and save it as A12. %%% Find the vector x that was rotated to give you vector b. %%% Save the vector x as A13 %%% Invert the R(3*pi/4) and save it as A14. %%% Find the angle theta that would give you this inverse %%% without having to do matrix operations, and save the angle %%% as A15