11.(12 points) Write a function in Matlab to generate a random m x n matrix A, where m and n are input parameters and the elements of A are integers between -5 and 5. Then, write a program in Matlab that uses this function to compute det(AA1) and det(A A) for 8 different random 3 x 5 matrices. What do you notice? 12. Extra credit: (10 points) Some graphics applications implement 2D image rotation using a series of three shear operations, because shearing is quick and easy to accomplish on a raster image: a shear transformation simply shifts all of the pixels in each row of an image to the right or left by a different specified amount. In fact, it can be shown that: cosO -sinf | | | all 1 011 1 a | 2 where a =-tan 1-1 and b = sin . 2) Use Matlab to visualize the sequence of shear transformations that accomplish a rotation by = You can start out by loading and displaying a standard image from the Matlab library. For example: 4 a imread( 'coins.png) figure imshow (a) Next, you will need to define each of the two different shear operations described in the equation above, but using homogeneous coordinates (so that the matrices are 3 x 3 rather than 2 x 2), and use it to define a spatial transformation structure that can be applied to data of type 'image. For