I have a set of linear equations and would like to find any feasible solution.  A simplex solution works in Case 1 below, but not in Case 2.  I would be grateful for any help.

Case 1: Find any feasible solution for the set of linear equations:
  a  +   b   +   c  = 5
  a  +   b  +  0c  = 4
0a +   b   +   c  =  4

Solution - a feasible (and unique) solution is a=1, b=3, c=1.

The following R code returns a feasible solution:
A3M = matrix(c(1,1,0,1,1,1,1,0,1),nrow=3)
b3M = matrix(c(5,4,4),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 = b3M, maxi = TRUE)


Case 2: Find any feasible solution for the set of linear equations
   a +   b   +   c  = 5
   a + 0b  +   c  = 2
0a +   b   + 0c  = 3

Solution - one feasible solution of many is a=1, b=3, c=1.  There are infinite possible solutions in Case 2.

However, the following R code fails to return any feasible solution:
A3M = matrix(c(1,1,0,1,0,1,1,1,0),nrow=3)
b3M = matrix(c(5,2,3),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 = b3M, maxi = TRUE)

The code returns the error:
Error in A.out[, basic] <- iden(M) : subscript out of bounds

Am I using the Simplex function incorrectly?  There may be a better way to approach the problem of finding a feasible solution.

Cheers,
Chris.

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