Node method to resolve a simple circuit, I’m stuck here
Make use of the Norton theorem!

BTW: The question seems to have an fault, since J_2 is given, but not  shown in the circuit diagram. 







simulate this circuit &ndash; Schematic created using CircuitLab

It's much easier!

Regarding your step

The matrix is 

$$ \mathbf{Y} \cdot \mathbf{V} = \mathbf{J}\, .$$

To get V, you have to invert the Y matrix:

$$   \mathbf{Y}^{-1} \mathbf{Y} \cdot \mathbf{V} = \mathbf{Y}^{-1} \mathbf{J} \\
\mathbf{V} = \mathbf{Y}^{-1} \mathbf{J} \, . $$