Start Typing in MATLAB 8.3 An other way of finding a basis for null-space of a matrix . Let B2 = [A21 /], you need to type this as : B2=[A2' eye(4) ] then find F2 = rref(B2) by typing F2=rref(B2) You will get a matrix of the form Note that in this matrix R is the rref(A') and IN is corresponding rref of I. Now check to see if the rows of N form a basis for the null-space of A2, by typing A2X1= F2(3,4:7) A2NS1= A2*A2X1' Repeat this for the second vector: A2X2= F2(4,4:7) A2NS2= A2*A2X2'