It's possible calculate the kernel of this matrix?

Question

I'm trying to calculate the kernel of this matrix in Matlab with this command

null(A)

But I receive this error

Empty matrix: 2-by-0 \begin{bmatrix} 5&-3\\ 1&1\\ 1&-1\\ \end{bmatrix}

I don't understand why I can't calculate the kernel of this matrix in Matlab

Answer 1

That is not an error message.

Z = null(A) is an orthonormal basis for the null space of A obtained from the singular value decomposition, in this case, the dimension of the nullspace is $0$. Your matrix has full column rank as we can see that the columns are not multiple of each other.

Answer 2

Note that the column vectors of the given matrix are linearly independent then null space contains only the zero vector $0_{2\times 1}$.