I am given the definition: "A matrix A is of full rank if and only if the vector $d$ for which $Ad=0$ is $d=0$."
I don't understand: if we have the matrix
$\begin{pmatrix}1&2&3\\ 4&5&6\\ 13&19&88\end{pmatrix}$
It is not of full rank, but what number other than $0$ can we multiply it by to get $0$? The last line is just an example that is independent of the first two.