Revision history [back]
 | 1 | initial version |
This is elementary linear algebra: the other solutions are obtained by adding vectors in the kernel... In Sage
M = matrix(QQ, [[1,2,3,4,5,6],[1,1,1,1,1,1],[1,-1,1,-1,1,-1],[1,2,1,3,1,4]])
x = vector(QQ, [6,1,-1,4])
v0 = M.solve_right(x)
K = M.right_kernel()
v1, v2 = K.basis()
From which you can build all solutions
sage: M * (v0 + 3*v1 - 19*v2) == x
True
sage: M * (v0 + 12*v1) == x
True
