We are looking for a kernel vector a = [ a 1 , a 2 , a 3 , a 4 ] such that the matrix product of M on a yields the zero vector [ 0 , 0 , 0 ] . The dimensional matrix as written above is in reduced row echelon form, so one can read off a kernel vector within a multiplicative constant: a = [ 2 0 − − 1 1 ] .