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An important problem in structural engineering is that of finding the forces in a statically

determinate truss $($see figure$).$ This type of structure can be described as a system of coupled

linear algebraic equations derived from force balances. The sum of the forces in both

horizontal and vertical directions must be zero at each node, because the system is at rest.

Therefore,

for node $1$:

${\displaystyle \underset{?}{\overset{?}{}}}{F}_H=-F_{1}cos30+F_{3}cos60=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_V=-F_{1}sin30-F_{3}sin60+F_{1,v}=0$

for node $2$ :

${\displaystyle \underset{?}{\overset{?}{}}}{F}_H=F_2+F_{1}cos30+H_2=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_V=F_{1}sin30+V_2=0$

for node $3$:

${\displaystyle \underset{?}{\overset{?}{}}}{F}_H=-F_2-F_{3}cos60=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_V=F_{3}sin60+V_3=0$

where $F_{i,v}$ is the external vertical force applied to node $i($where a positive force is upward$).$

Express this set of linear algebraic equations in matrix form and then use MATLAB to solve

for the unknowns.