We write the first equation so that the constant term is on the right hand side:

F1 sin 69.3° − F2 sin 71.1° − F3 sin 56.6° = -926

In matrix form, we write the equations as:

forcesforces

So the solution for the system is:

solutionsolution 2solution 3

So

F1 = 425.5 N

F2 = 1079.9 N

F3 = 362.2 N

This is very easy and quick in Scientific Notebook!