Thanks. I had actually put -1/20 in the bottom left as I had gotten the correct answer but a positive result and found my error in equation 7. I had just forgot to update that error in the table. I had also forgot to update (In row 7, column 8 you have 12/20; it should be -12/20) mistake in the table, but had it in the calculator. As for all the other I was unaware. It is really amazing how you can mess up so bad and not even realize. This has opend my eyes and I will attempt to self verify more often. Thanks again.Here is the matrix you derived and its solution showing all of your variables, not just Ix. I checked the numbers in this matrix several times and I believe I'm using the same values shown on your work sheet.
View attachment 149422
To 8 digits, you got Ix = +0.37930552 A. I'm showing more digits than you did for a reason that will be explained. Notice that the sign which the matrix arithmetic delivers is positive even though you showed a result with a minus sign. Did your calculator actually return a result with a minus sign?
Each row in the matrix corresponds to one of your equations, i.e., row 1 is Eq. 1, row 2 is Eq. 2, etc.
In row 1 (equation 1) you left out the -12/20. This should have been added to the far right column.
In row 5, column 4 you have 1/22; it should be -1/22
In row 7, column 1 you have 1/20; it should be -1/20
In row 7, column 8 you have 12/20; it should be -12/20
If these changes are made this is the result:
View attachment 149423
Now the result for Ix is -0.37869988. Notice that if the magnitude of your result and of this result are rounded to 3 places, the result is .379
Apparently the errors you made sufficiently compensated for one another that your final result magnitude, rounded to 3 digits is the same as the rounded magnitude with your errors corrected. This could lead one to overlook the errors and think you had done everything correctly. The sign difference is another matter.