I found it impossible to do so some years ago, and my account has been left dormant ever since as a result. I'm sure I'm not the only person who faced this problem.
YES! It was impossible for me to close my account.
I emailed them repeatedly and they claimed my account was closed. Then someone sent me a message (because my account was still appearing on the site..) and it REOPENED my account and I started getting email about it again. LinkedIn is the WORST.
https://help.linkedin.com/app/answers/detail/a_id/63