Matrices make Statics easier

From the diagram, we obtain the following equations (these equations come from statics theory):

Vertical forces: F₁ sin 69.3° − F₂ sin 71.1° − F₃ sin 56.6° + 926 = 0

Horizontal forces: F₁ cos 69.3° − F₂ cos 71.1° + F₃ cos 56.6° = 0

Moments: 7.80 F₁ sin 69.3° − 1.50 F₂ sin 71.1° − 5.20 F₃ sin 56.6° = 0

Using matrices, find the forces F₁, F₂, & F₃.

Answer:

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:

So the solution for the system is:

So F₁ = 425.5 N, F₂ = 1079.9 N, and F₃ = 362.2 N .

I checked the link that Noubar used and I liked this problem in Statics. Why did I like it? Because I'm an engineering student and I took that course last semester and I hated it because of such long calculations: we didn't use matrices in such problems, we used to solve them in typical long methods by replacing the unknowns in function of each other, and it never ended..

Now I wish if I only knew about matrices last semester.. Statics would have been much easier especially for systems of 4 equations and 4 unknowns (and even more: 5 or 6) that a regular calculator cannot solve..

Source : http://www.intmath.com/matrices-determinants/6-matrices-linear-equations.php

Tony Al-Rajji.