So, here's what I got

Current 1-

\( 135 + 2I_1 +20(I_1+I_2) + 3(I_1+I_3) = 0\)

\( 25I_1 + 20I_2 + 3I_3 = -135 \)

Current 2-

\( 10i_0 + I_2 + 20(I_2+I_1) + 4(I_2-I_3) = 0\)

\( I_1+I_3 = i_0 \)

\( 10(I_1 + I_3) + 20(I_2+I_1) + 4(I_2-I_3) = 0 \)

\( 30I_1 + 24I_2 +6I_3 = 0 \)

Current 3-

\(5I_3 + 4(I_3 - I_2) + 3(I_1+I_3) = 0 \)

\(5I_1 - 4I_2 + 12I_3 = 0\)

25 20 3 | -135

30 24 6 | 0

5 -4 12 | 0

I wind up with

I1 = -87.75

I2 = 92.8125

I3 = 67.5.

But to find the branch current, you have to sum I1 and I2 together, which would give me a total current of 5.0625 running through that branch. Using my power expression, p=vi^2, I'm getting 512.57 W....according to the back of the book, I'm looking for 259.2 W. Do you see any errors in there?

Thank you guys for your help!

*The final, correct equations are-*

*Mesh 1*

\( 135 + 2I_1 +20(I_1+I_2) + 3(I_1+I_3) = 0\)

\( 25I_1 + 20I_2 + 3I_3 = -135 \)

*Mesh 2*

\( 10i_0 + I_2 + 20(I_2+I_1) + 4(I_2-I_3) = 0\)

\( I_1+I_3 = i_0 \)

\( 10(I_1 + I_3) + I_2 +20(I_2+I_1) + 4(I_2-I_3) = 0 \)

\( 30I_1 + 25I_2 +6I_3 = 0 \)

*Mesh 3*

Current 3-

\(5I_3 + 4(I_3 - I_2) + 3(I_1+I_3) = 0 \)

\(3I_1 - 4I_2 + 12I_3 = 0\)

*The final matrix would look like...*

25 20 3 | -135

30 25 6 | 0

3 -4 12 | 0