The statically determinant truss structure is under loading conditions, as shown in the figure below. The truss has $5$ members with equal cross$-$sectional areas: members $[1],[2],[3],[4],$ and $[5].$

a$.$ Draw a free$-$body diagram at nodes $1,2,3,$ and $4$ to illustrate all forces. $($Assume all member forces are in tension for consistency in sign convention.$)$

b$.$ Formulate $8$ force equilibrium equations $(2$ equations per node$).$

c$.$ Get the member forces $($F$1,$ F$2,$ F$3,$ F$4$ and F$5)$ and reaction forces

$($R$2$H$,$ R$2$V$,$ and R$4$V$)$ by solving Linear Algebraic Equations. Use matrix inversion.

d$.$ As the load applied at node $3(600$N$)$ increases incrementally, which member will fail first?

Note: From the material testing, the metal rod used in the truss member failed at $3,000$N$.$ Assume small deformation $($the deformations of the members are negligible compared to the original lengths of the members, so the angles between the members are the same$).$