$2\mathrm{.}2$ Computing Eigenvectors Before running your code on the trench depth data, it is good to develop the code using a smallish matrix for which you know the eigenvalues and eigenvectors. Do not include the testing data in the report. $1.$ Code your own algorithm to find the first eigenvector and eigenvalue of ATA, where A denotes the depth matrix. To do this, $($a$)$ First begin with a random guess vector of the correct size and magnitude one. $($b$)$ Apply ATA to that vector, and then divide the result by its magnitude to make sure it$$s still magnitude one. That is your updated guess. $($c$)$ Repeat the two steps above until the vector stops changing