What is a matrix clause?
The source below says this about a clauses in gneneral.
"One clause may be embedded within another, that is, it may be used as a constituent part of another clause. Such a clause is called an embedded clause (or a subordinate clause) and the clause within which it is embedded is called the matrix clause. The embedded clause is a constituent of the matrix clause. A clause that could occur on its own as a sentence is called a main clause. In the following examples the embedded clauses are given in boldface; each of the matrix clauses is also a main clause: The boy who came is his cousin. I told him that I would go.
To explain this again, the matrix clause is an independent clause that could stand on its own and make perfect sense. It is called a matrix clause when there are subordinate clauses in the sentence as well. Subordinate clauses can appear anywhere in a sentence so it is important to note the subordinating conjunction or relative pronoun that usually introduces them if you are trying to identify the distinct clauses that make up a complete sentence. In the example sentences above, "who" is a relative pronoun/subject of the verb "came." That clause can't stand alone -- it is subordinate to the rest of the sentence -- it is part of the idea, but not the whole idea. In the other example, "that" is is a subordinating conjunction introducing a subordinate clause. Again, that part of the sentence can't stand alone, but provides more information and completes the thought of the independent (matrix) part of the sentence.
Matrix clauses are co-extensive sentences i.e they are not subordinate to any other sentence in relation.
For example:1>How are you?
--> I'm fine.
Here i'm fine may be stated as...
--> I think i'm fine.--> This is a extensive sentence/Matrix clause.
-->I'm fine. --> This is a sub-ordinate clause.