If my reduced row echelon of the matrix looks like
\begin{pmatrix} 1 & 0 & 0 & 0 & 0 &0\\ 0 & 1 & 0 & 0 &0 &0\\ 0 & 0 & 0 & 0 &0 & 0\\ 0 & 0 & 0 & 0 &0 & 0\\ 0 & 0 & 0 & 0 &0 &0\end{pmatrix}
then using the linear algebra terminology I would say that the dimension or the degrees of freedom is two correct?
What is meant by $Ker(M) \neq 0$? I don't understand this and would need an example. Also if the $Ker(M) = 0$ is the matrix $M$ invertible? Does the converse of this statement hold? Please help I want to get this material to pass my linear algebra class