To remove the header image of the Twenty Eleven theme on other pages then your homepage, change the following code in header.php (in wp-content/themes/twentyeleven)
Before:
<?php
// Check to see if the header image has been removed
$header_image = get_header_image();
if ( ! empty( $header_image ) ) :
?>
After:
<?php
// Check to see if the header image has been removed
$header_image = get_header_image();
if ( ! empty( $header_image ) && is_front_page() ) :
?>