Using Eclipse with a pre-existing C Makefile - c

Question

I wrote a makefile which works fine in shell (ubuntu), but I can't manage to run it from eclipse.
I created a makefile in eclipse, which is seen under DEBUG directory of the relevent project.
In Run/Debug settings I defined in Main tab in C Application: Debug/projectname, and in Project: projectname, Build configuration:Debug. (which now I see it gives me an error of not executable file so I change it to the main.o file).
in C/C++ Build , in Builder Settings I checked use default build command and unchecked Generate Makefiles Automatically. Build directory is ${workspace_loc:/projectname}
What should I do now? How make command can be run?
What is make target? I tried to create one and then build it, but I don't see how it connects to my makefile. Should make target be done from view target of from right click on the project?
From make target view I created new target and when I do 'build target' I get
make mat
make: *** No rule to make target `main.c', needed by `main.o'. Stop.
So it seems to read the right makefile, but what is "No rule to make target `main.c' "? the makefile is:
mat:main.o mat.o
gcc -ansi -lm -Wall mat.o main.o -o mat
main.o:main.c mat.h def.h
gcc -ansi -pedantic -Wall -c main.c
mat.o:mat.c def.h
gcc -ansi -pedantic -Wall -c mat.c