We are given a system of three equations with three variables (forces $FAB$, $FAC$, and $FAD$):

$0.358FAB + 0.188FAC - 0.37FAD = 0 \quad \text{(1)}$ $-0.268FAB + 0.282FAC - 0.092FAD = 0 \quad \text{(2)}$ $-0.894FAB - 0.94FAC - 0.924FAD + 3500 = 0 \quad \text{(3)}$

We need to solve for $FAB$, $FAC$, and $FAD$. I will use a matrix method (Gaussian elimination or another numerical technique) to solve this system. Let's proceed by solving it step by step.

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If you'd like to proceed manually or discuss the steps further, feel free to ask! Meanwhile, here are some related questions you might want to explore:

1. How do you perform Gaussian elimination to solve a system of equations?
2. What are the steps to set up a matrix for solving linear equations?
3. How does substitution work for solving systems of linear equations?
4. Can we always use a matrix method to solve systems of equations?
5. What is the significance of each variable in a force equation like this?

Tip: When dealing with systems of equations, consider simplifying each equation or using substitution to reduce complexity before applying a matrix solution.