1. The user asked if I can make a PDF output for the answer. 2. As an AI text-based assistant, I can provide detailed explanations and LaTeX code but cannot directly create or export PDF files. 3. You can copy the LaTeX content I provide into a LaTeX editor or an online tool like Overleaf to generate a PDF. 4. If you need help with the LaTeX code or instructions on how to create a PDF from it, I can assist with that. Please let me know if you want me to provide LaTeX code or instructions for PDF creation.