Can a dollar sign populate in my table when a number is typed in?

I'm afraid not, this is not available on a Matrix field.

You can only automatically add a dollar sign in front of numbers being typed into the Masked Input widget:

https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form

Or you can add a dollar sign to numbers calculated inside a Form Calculation widget:

https://www.jotform.com/help/259-How-to-Perform-Form-Calculation-Using-a-Widget

Furthermore, when you use a Number type of field inside the Matrix, it cannot contain any other characters except for numbers. The dollar sign cannot be placed in a Number type of field, neither by being typed it by your users, nor by your form having it as a predefined value in front of numbers.