Solution 80: Slaying a Monstrous Determinant using Second Differences
- Published on Feb 21, 2019
- We have a quadratic sequence embedded within the determinant -- Can we take advantage of this?
This particular problem was inspired by one of the sections on determinant in "Linear Algebra Gems: Assets for Undergraduate Mathematics," a marvelous book I incidentally came upon in a university library, containing many fascinating articles on linear algebra. The article on determinant essentially used the techniques presented in the video, along with a slightly more sophisticated algebra, to derive the formula for a determinant of a square n x n matrix with its terms forming a sequence with (n-1)st common difference. I realized that the formula can be extended to cover the case where each term is written as a product of the aforementioned sequence and a geometric sequence, and the result was the problem in the video. If you are interested in exploring some "non-standard" yet fascinating theorems and ideas from linear algebra, I encourage you to check out the book from the nearest university library. =)
Congratulations to Avi Uday, Benjamin Wang, aby p, Arun Bharadwaj, Andre Ben, Jaleb, 張惟淳, Serengeti Ghasa, Varun Shah, and mstmar for successfully solving this math challenge question! Avi Uday was the first person to solve the question.
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