Problem 2: Determinants

write code in python, sagemath

Grading criteria: correctness of code and explanations.

2a. Implement a function called my_det that calculates the determinant of a matrix recursively using expansion by cofactors. The Matrix methods delete_columns and delete_rows may come in handy. You can assume that your input is a square matrix.

2b. Check that your function agrees with Sage's built-in function on a random 5 by 5 matrix over

2c. Do some timings for random matrices over for comparing your function and Sage Math's built-in function. Make a single plot containing both sets of results.

2d. Explain the results of 2c in terms of the asymptotic complexity of the two methods.