Combine upper, lower, and diagonal matrix?

[sarahfh]

If you have a matrix that is a combination of a diagonal, upper, and lower matrix - what is the best way to solve it? (I use matlab for matrix work)

Example:
5 1 0 0 x1 1
-1 5 1 0 x2 2
0 -1 5 1 x3 3
0 0 -1 5 x4 4

Is it possible to solve the upper triangle and lower triangle and then combine them?
Would it be possible to solve it quicker if the all three diagonals were the same (as above)?

[weetabixharry]

I can't understand the example you have written. What does an "x" denote?

What do you mean by "solve" a matrix? Please clarify your example and I think someone will be able to help you.