listed below for each problem. Read the MATLAB documentation if you are not familiar with a function or an operator. You do not need to perform any error checking for these functions.

Problem $1$: Construct a MATLAB function $[$A$,$ a bar$]=$ ubitname final$\_$p$1$ which reads all

png images contained in the same directory as the function. This function returns the matrix A which corresponds to the matrix A above and the vector a bar which corresponds to vector a above. You can use the following MATLAB functions for this problem: dir, sum, length, double, and imread. All of the images are guaranteed to be grayscale images and all will have the the same size m x n$.$

Problem $2$: Construct a MATLAB function $[$x$,$ U$]=$ ubitname final p$2($A$)$ which returns the

matrix X which corresponds to the matrix X described above while U is the matrix U from the

SVD of A$.$ You are allowed to use the following MATLAB functions for this problem: SVD and transpose $($or it's short$-$hand call$).$

Problem $3$: Construct a MATLAB function i $=$ ubitname final p$3($f$,$ X$,$ U$,$ a bar, tol$)$

which attempts to perform image identification. The input f is a string to a file name in the same directory as this function, X is the corresponding output from Problem$-2,$ U is the corresponding output from Problem$-2,$ a bar is the corresponding output from Problem$-1,$ and tol is the tolerance to use when identifying images. If the image f exists in the original N images used in Problem$-1$ then i will equal the corresponding image number. If the image f does not exist in the original N images then the function should return $1=0.$ You are allowed to use the following MATLAB :$28$ PM

functions for this problem: norm, double, and transpose $($or it's short$-$hand call$).$

The image

referenced by f will be a grayscale image of size m $\backslash$times n$.$

To help students five test images have been included. No aid will be provided on how to use these test images. The use of any unauthorized functions will result in an appropriate sanction.