You will have to do a lot of modifications on this one.
We are going to modify header.php file
Firstly move this piece of code from header tag file to below body tag
<?php if ( get_header_image() ) : ?>
<a href="https://wordpress.stackexchange.com/questions/152110/<?php echo esc_url( home_url("https://wordpress.stackexchange.com/" ) ); ?>"><img src="<?php header_image(); ?>" class="header-image" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" /></a>
<?php endif; ?>
wrap this code in a div
<div class="header-full-width">
<?php if ( get_header_image() ) : ?>
<a href="https://wordpress.stackexchange.com/questions/152110/<?php echo esc_url( home_url("https://wordpress.stackexchange.com/" ) ); ?>"><img src="<?php header_image(); ?>" class="header-image" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" /></a>
<?php endif; ?>
</div>
Now add css
.header-full-width img {
width: 100%;
}
This should do the trick.