Problem 1 Principal component Analysis (PCA) is a mathematical tool that is used for analysing components of the data according to their weight on the data distribution. It is widely used for changing the basis of data and/or dimen- sion reduction. In order to determine the principle components and their weights eigenvalues and eigenvectors are used. (a) Search and explain in details what the role of eigenvalues and eigenvectors in PCA is. (b) Write a MATLAB code for PCA. For that purpose you are not allowed to use built-in functions for PCA. Please include comments on your code. Otherwise you will get half credits