MHB Kirchoff's Law equation 3 unknowns Help

AI Thread Summary
To solve the system of equations derived from Kirchoff's law, the initial equations for currents i1, i2, and i3 are provided. The user has performed row operations on the augmented matrix to simplify the equations but seeks assistance in completing the solution. The final matrix indicates that further back substitution is needed to find the values of i1, i2, and i3. The key steps involve continuing with the row reduction and then solving for the unknowns using back substitution. Completing these steps will yield the values for the currents in the circuit.
JonB
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Please could somebody help me with this Kirchoff's law question with explanations/working out? I've been on it for hours and cannot see where I'm going wrong!

Q. An electrical circuit comprises three closed loops giving the following equations for the currents i1, i2 and i3.

i1 + 8i2 + 3i3 = -31
3i1 - 2i2 + i3 = -5
2i1 - 3i2 + 2i3 = 6

Solve for i1, i2 and i3

Any help appreciated!
 
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We have
$$
\left[\begin{array}{rrr|r}
1 &8 &3 &-31 \\
3 &-2 &1 &-5 \\
2 &-3 &2 &6
\end{array} \right]_{\begin{array}{rr}-3R_1+R_2 \mapsto R_2 \\ -2R_1+R_3 \mapsto R_3\end{array}} \to
\left[\begin{array}{rrr|r}
1 &8 &3 &-31 \\
0 &-26 &-8 &88 \\
0 &-19 &-4 &68
\end{array} \right]_{-\frac{19}{26}R_2 + R_3 \mapsto R_3} \to
\left[\begin{array}{rrr|r}
1 &8 &3 &-31 \\
0 &-26 &-8 &88 \\
0 &0 &\frac{24}{13} &\frac{48}{13}
\end{array} \right].
$$
Can you finish?
 
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