@David, do you do this on any site and which method do you use? What site(s)?
My website is meant as a learning tool, I only write posts and create child themes when I think something might be of use to a few others.
I do not get to use much of the code myself as I do not create themes for others, most posts and themes are created after reading posts on this forum.
Please make sure it is: Twenty Eleven Header Image using is_category ...
Most of the posts on my website have a download, the downloads on all three linked posts are twenty eleven child themes, and the files include category.php, header.php, functions.php, where the changes are called.
The idea is that you have a fully working child theme example to test and all the code you need to merge with your own theme.
Looking at your website you have your themes folder as 'wp-content/themes/twentyeleven/', if you have modified any files then you may lose the changes.
Later this week there is a scheduled new WordPress release with a new twenty eleven theme, if you update the twenty eleven theme, your themes folder files will be replaced.