Using sage to check if a vector is in a matrix's null space
I want to check if a given vector is inside a matrix's null space.
Here is what I have done:
#Define a matrix A=Matrix([[1,-1,2,-1],[2,1,-2,-2],[-1,2,-4,1],[3,0,0,-3]],ring=QQ) #Free variables to be used in the given vector var('s t') #The null space of the matrix A ns=A.kernel() s=2 t=1 #Create a vector ans=s*vector([1,0,0,1])+t*vector([0,2,1,0]) #If ans is in the null space of A, then A*ans is the 0 vector print A*ans #If A*ans is the 0 vector, then the following should be true too print ans in ns
I had expected the last print statement to be true since A*ans results in a zero vector, hence ans is in the null space of A.
Why isn't this the case?