Consider the truss structure loaded as shown. Given that the cross$-$sectional area is the same for all elements $A=1i{n}^2,$ length $a=50in,$ Young's modulus $E=46*{10}^6,$ applied force $P=75,000lb,$ and prescribed downward displacement $=0\mathrm{.}5in,$ solve by hand and determine:

a$)$ all nodal displacements

b$)$ all support reaction forces

c$)$ stress in the element AB

Use elimination approach and engineering software to find the solution vector for the reduced global system of linear equations. Make sure to describe your solution steps.