3x3 matrix Eigenvalues/Eigenvectors in graded quiz, but not taught?

I love this course, have been learning a lot, but then when you hit question 7 of the week 4 Eigenvalues and Eigenvectors graded quiz, you see a 3x3 matrix and are instructed to “Given matrix P select the answer with the correct eigenbasis.” It has a hint that says “Hint: First compute the eigenvalues, eigenvectors and contrust the eigenbasis matrix with the spanning eigenvectors.” (I assume that’s a typo and “contrust” is meant to be “construct”).

I honestly thought I skipped a video, because nowhere in the course did it describe how to solve eigenvalues and eigenvectors for 3x3 matrices, which seem to be a lot more involved. It seems like the lecture material and quizzes were written by 2 separate people. So I’ve been sitting on this question 7 for over a day while I’m researching how to solve it in a variety of places.

It looks like you need 30 minutes of additional instructional content added to the course to cover the material:

Alternatively, you could change the quiz question to a 2x2 matrix, which is what’s covered in the lecture content.

If I’m missing something, which is highly probable, let me know where I’ve stumbled I’m not a math major, so perhaps it assumes you already know how to do some of this stuff? But that doesn’t make sense because it teaches you Eigenvalues and eigenvectors as if you don’t know them at all.

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Actually, I was able to find the eigenvalues by following the same steps in the lecture. After calculating the det(P) you get a factored polynomial from which you can get the eigenvalues directly.

What they didn’t cover is what to do in the case you have two eigenvalues with the same value, which appear in Question 7.

how to change the question to a 2x2 matrix?

He’s referring to the course authors changing the materials. It’s not something a student can do.