## Instruction
Inspired by the math content, create a college-level math problem. 

## Math Content
<EXTRACT>

## Guidelines
[Problem]: Draft a self-contained, college-level math problem inspired by the math content. It should be intellectually stimulating and designed for an audience familiar with advanced mathematics, such as Calculus, Linear Algebra, Abstract Algebra, etc. Ensure the problem includes all necessary information for solving it. Aim for a problem statement around 100-150 words.
[Solution]: Provide a step-by-step solution to your problem, around 250-350 words long. The solution should clearly explain the reasoning, mathematical principles, and steps used. Call out any key theorems or properties being applied at each step.

## New Problem