Dry run \(\alpha\)

Write a list containing the information of the Porphyrian Tree. Then select the insensitive part of the tree.

Dry run \(\beta\)

Write a function that, given a matrix \(A\) and an integer \(n \geq 0\), computes the product of the eigenvalues of the power \(A^n\).

Dry run \(\gamma\)

1. Read the CSV file rank.csv into a data frame with function read.csv()
2. select the rows with rating above the 3rd quartile (75% quantile) and put the result in a new data frame called top (use quantile() function)
3. select the rows with rating below the 1st quartile (25% quantile) and put the result in a new data frame called bottom (use quantile() function)
4. build a nested data frame with the top and bottom data frames created above an take a look at its structure with function str()
5. retrieve the teams of the top data frame from the nested data frame