Consider the lexicographic order .
Reduce the matrix in row echelon form using row operations; The polynomial set produces the same ideal, and cannot be reduced any further.
Thus, this set (and equivalently the starting set) is a Groebner basis.
Consider the lexicographic order .
Reduce the matrix in row echelon form using row operations; The polynomial set produces the same ideal, and cannot be reduced any further.
Thus, this set (and equivalently the starting set) is a Groebner basis.