Code-First approach, location of database and all instances (v110, etc)

Question

I'm following this tutorial to create a Code-First Database.
After installing EF and creating those first basic classes it says:

Run your application and you will see that a MigrationsCodeDemo.BlogContext database is created for you.

Well, I have VS2013 Pro with all the SQL Servers installed (full installation of VS2013 Pro).
Now as you can see from the image below, I can't find my database after running the program as the tutorial is suggesting. When I try to do the migrations part of the tutorial, I indeed get the error it supposed to get, implying that somewhere the database actually has been created. I just am not able to find it.
Where is it located?

Edit: added App.config

<?xml version="1.0" encoding="utf-8"?>
<configuration>
  <configSections>
    <!-- For more information on Entity Framework configuration, visit http://go.microsoft.com/fwlink/?LinkID=237468 -->
    <section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=6.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
  </configSections>
  <startup>
    <supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5" />
  </startup>
  <entityFramework>
    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
      <parameters>
        <parameter value="mssqllocaldb" />
      </parameters>
    </defaultConnectionFactory>
    <providers>
      <provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
    </providers>
  </entityFramework>
</configuration>

Answer 1

The physical master database files are at

C:\Users\<user>\AppData\Local\Microsoft\Microsoft SQL Server Local DB\Instances\v11.0  

The DB files are simply in C:\Users\<user>

You can also connect to localdb using SSMS by using server (localdb)\v11.0 and delete the database from there.

The official documentation is here http://msdn.microsoft.com/en-AU/library/hh510202.aspx

Edit by QuantumHive:
I finally figured out that the Database can be found in the instance called MSSqlLocalDb which Entity Framework added by default in my App.config. I now have a visualization of the database in Visual Studio:

I'm guessing those tutorials are old and referring to the v11.0 instance, which perhaps and older version of EF added that by default at the time.