One of the features of the free Matrix Agent Web page is the ability of a visitor to sign up to become a contact of that particular agent.
In the top right corner of the page, there will be a link (Sign up with...) that visitors can click:
They can then enter their contact information and a message to the agent:
If you are an agent using the Matrix Web page, make sure to keep an eye on the Contact Requests widget on the Matrix home page. That is where you will be notified if any visitors use the Sign up with link on your web page.