How can I use Gauss elimination to zero out the elements of a block system?

[Scootertaj]

1. See the following picture:
http://imageshack.us/photo/my-images/715/math5610.jpg/

Essentially what I'm trying to do is solve a linear block system.
I have got to the point where I now need to "add multiples of the top rows to clear out C."
Now, I'm sure this is the easy part as I've already had to make a Matlab program to solve a tridiagonal system, but I just can't figure out how I essentially eliminate C.

Known: I (identity), E, x1,b3,C,D,x2,b2.



Like I said, I'm sure I'm making this easy step very difficult, but I don't know where to proceed :/

 

[Scootertaj]

Just a bump. I'm sure this is easy LA I can't figure out.

 

[Scootertaj]

Turns out the image isn't showing, sorry for another post:

 

[hotvette]

I think all they are saying is that you can use Gauss elimination to systematically zero out the elements of C. For example, let's say the upper left element of C is c₁. Multiply the top row of the matrix by -c₁ and add it to the row containing c₁. Now the upper left corner of C is zero. Next pick the proper row in the upper part of the matrix to zero out the next non-zero term of C, and so on until all elements of C are zero. It might help to write out a small made up problem (e.g. each sub-matrix is a 2x2) and work through the steps by hand.

 

[Scootertaj]

I think all they are saying is that you can use Gauss elimination to systematically zero out the elements of C. For example, let's say the upper left element of C is c₁. Multiply the top row of the matrix by -c₁ and add it to the row containing c₁. Now the upper left corner of C is zero. Next pick the proper row in the upper part of the matrix to zero out the next non-zero term of C, and so on until all elements of C are zero. It might help to write out a small made up problem (e.g. each sub-matrix is a 2x2) and work through the steps by hand.

Ya, that's what I was figuring, but I was hoping there would be an easier way to do it (I'm programming it in Matlab).
Obviously, a double loop will work and get the job done, but was looking to see if there was a slicker way to do it.