# Finding solution set of system of linear equations. Classic List Threaded 3 messages Open this post in threaded view
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## Finding solution set of system of linear equations.

 I have a simple system of linear equations to solve for X, aX=b: > a      [,1] [,2] [,3] [,4] [1,]    1    2    1    1 [2,]    3    0    0    4 [3,]    1   -4   -2   -2 [4,]    0    0    0    0 > b      [,1] [1,]    0 [2,]    2 [3,]    2 [4,]    0 (This is ex Ch1, 2.2 of Artin, Algebra). So, 3 eqs in 4 unknowns. One can easily use row-reductions to find a homogeneous solution(b=0) of: X_1 = 0, X_2 = -c/2, X_3 = c,  X_4 = 0 and solutions of the above system are: X_1 = 2/3, X_2 = -1/3-c/2,  X_3 = c, X_4 = 0. So the Kernel is 1-D spanned by X_2 = -X_3 /2, (nulliity=1), rank is 3. In R I use solve(): > solve(a,b) Error in solve.default(a, b) :   Lapack routine dgesv: system is exactly singular and it gives the error that the system is exactly singular, since it seems to be trying to invert a. So my question is: Can R only solve non-singular linear systems? If not, what routine should I be using? If so, why? It seems that it would be simple and useful enough to have a routine which, given a system as above, returns the null-space (kernel) and the particular solution.