I'm solving the following system of linear equations,
Ax = b, some of the x's are knowns.
-12 12 0 0 0
0 -1 1 0 0
0 0 -0.5 0.5 0
0 0 0 -17 17
x = [x1 x2 x3 x4 x5]
b = [b1 0 0 0 b5]
When some of the variables are known, say x1 and x5 are known, the system can be reduced in terms of the known variables. However, when there are around 50 variables and 5 are known re-writing the matrix in terms of the known variables is difficult.
I would like ask for suggestions on alternate ways of solving these kind of linear systems in which the values of a few variables are known.