What is agile?
>Agile is neither top-down nor bottom-up: it is outside-in. The focus is on delivering value to customers. The customer is the boss, not the manager. page 
Is it even possible for large or old corporations to transform themselves and become agile?
>The primary goal of making money for shareholders is at odds with the values of Agile where the primary focus is on delivering value to the customer. In Agile, making money is the result, not the goal. When those two different goals are espoused in different parts or different levels of the organization, there is permanent friction. Unless this issue is resolved, the adoption of Agile at the team level is unlikely to stick.