/* Define a A matrix */
a={1 5 7 9 3,2 6 4 8 10};
/* Define the right-hand-side */
b={5,9};
/* Solve the system in row-reduced form */
z=rref(a~b);
xstar=z[.,6]|zeros(3,1);
xstar;
a*xstar;
/* Compute the Nullspace matrix */
null(a);
/* Choose a projection direction */
p={1,10,3};
/* Generate the new point */
x=xstar+null(a)*p;
x;
/* Check for feasibility */
a*x;