Problem solving a exercise for exam

[97hilfel]

Hello everybody,
I am currently studing for my electronics exam and I Cant figure out where some certain values come from, It would be really kind if somebody could explaim my the solution of the exampls (privided in the pdf).
Its example 62 with the following question:
Calculate the following system using the nodal analysis the equationsystem for the voltage U_a.
The line after the matrix:
The outputvoltage U_a is:
Ua=U_30.
I dont understand the following things in the matrix:
- Why is in field (1, 2) -G_3-50G_4 and not in (2,1) also?
- Why is in field (2, 2) 51*G_4? where does the 51 come from?

[ebastler]

Hmm, something seems to be missing in the definition of that example.
Where are U10, U20 and U30 in the diagram?

[97hilfel]

They represent the voltages from node 1 to 0, 2 to 0 and 3 to 0

[Andy Watson]

Look at the definition of the third voltage source. It is defined as \$50 U_3\$. Redefine \$U_3\$ as \$U_{20}-U_{10}\$, (as in the diagram) and you should see where the \$-50G_4\$ and \$+51G_4\$ terms come from. (I may have mixed my signs but I'm sure you can cope with that).