Scalable serverless event-driven architecture (EDA) is a design pattern that allows for the creation of highly available and cost-effective applications using AWS services. This architecture is built on the principles of serverless computing and event-driven programming and can be used to create applications that can automatically scale to meet the needs of the business.

In a serverless EDA, events are the driving force behind the application. These events can be generated by a variety of sources, such as user interactions, changes to data, or system events. Each event triggers a series of AWS services to respond and take action, ultimately resulting in a change in the state of the application.

AWS Lambda is a key service in building a serverless EDA. Lambda allows developers to run code without the need to provision or manage servers. Instead, the cloud provider is responsible for running the code and scaling it as needed. This can greatly reduce the cost and complexity of building and running applications.

AWS event sources such as S3, DynamoDB streams, Cloudwatch, Kinesis streams, etc can be used to trigger a Lambda function when a specific event occurs. For example, a new image uploaded to an S3 bucket can trigger a Lambda function to process the image and store it in a different S3 bucket.

Another important aspect of serverless EDA is the use of messaging queues, such as Amazon Simple Queue Service (SQS), to manage the flow of events between different parts of the system. This allows different components of the application to be decoupled, improving scalability and fault tolerance.

AWS services such as DynamoDB and S3 can be used to store and retrieve data in a serverless EDA, while AWS API Gateway and AppSync can be used to expose the data to client applications.

AWS Step Functions can also be used to coordinate multiple Lambda functions and other AWS services together to build a complete workflow for an application. For example, Step Functions can be used to process an image uploaded to S3, by triggering multiple Lambda functions and other AWS services like Kinesis and Lambda.

To sum up, a scalable serverless event-driven architecture is an effective structure for constructing applications on Amazon Web Services (AWS) that can modify itself to meet the requirements of the company. By taking advantage of AWS Lambda, events sources, messaging queues, and other AWS services, coders can forge applications that are highly available, economical, and straightforward to supervise. In addition, the organization and handling of workflows are more straightforward through AWS Step Functions and it permits for the building of complex applications by utilizing other AWS services like Kinesis and Lambda.