MET

Welcome to the Machine Learning Engineering teams' online technical interview - thanks for taking the time!

This challenge aims to highlight a few different areas of your technical skillset. We'll be looking for:

• Collaborative communication and problem-solving (soft skills)
• Proficiency and prowess with your programming environment (medium skills)
• The ability to break down and implement a solution to the problem (hard skills)

Challenge

As a part of the Machine Learning Engineering team, you've been tasked to implement a function that can calculate the determinant of a n by n matrix.

• We've stubbed out a function within the det.py file.
• We've written some basic unit tests in the test_det.py file.

You can use Google etc to look up what the matrix determinant is and any Python / library API documentation.

NOTE: We do not expect you to implement an optimal solution, nor do we expect you to come up with a complete solution within the time frame. Implementing a naive solution that can be easily communicated.

Hints (only if required)

If you get stuck, here's some extra help to push you in the right direction.

Hint 1

We like this simple explanation of how to calculate the matrix determinant.

• https://www.mathsisfun.com/algebra/matrix-determinant.html

Can you see how the 3 by 3 relates to the 2 by 2?

Would a recursive algorithm be useful here?

Hint 2

We know that a recursive algorithm calls itself. If we're not careful we may continue to call ourselves until our program runs out of memory...

What would our stopping condition be? Can we implement this?

Hint 3

Let's break down the 3 by 3 case.

We can see that the 3 by 3 case is each value of the first row multiplied by the determinant of the 2 by 2 sub-matrix.

Let's first iterate just this first row. How is the position of the current value we're iterating related to the formation of the sub-matrix?