Solve step by step using legible handwriting, if you wish you can use python. Explaining

the transformation matrices, and writing the formulas.

Solve the truss presented in the figure whose elements have a cross section of area $0\mathrm{.}01$ m $2$

and a material with elasticity modulus $E$:$2{10}^{8}k\frac{N}{m}2.$

Using the stiffness method:

a$)$ Nodal displacements in global coordinates.

b$)$ Reactions in global coordinates.

c$)$ Axial force in each bar

$\{[u_1^{*}],[u_2^{*}],[v_2^{*}],[u_4^{*}],[v_4^{*}],[u_5^{*}]\}=\{[2\mathrm{.}1484{10}^{-5}],[-8\mathrm{.}4303{10}^{-5}],[-1\mathrm{.}7784{10}^{-4}],[-4\mathrm{.}1607{10}^{-5}],[-2\mathrm{.}2047{10}^{-4}],[1\mathrm{.}5580{10}^{-4}]\}m,\{[F{Y}_2],[F{x}_3],[F{Y}_3],[F{x}_4],[F{Y}_4],[F{x}_5],[F{Y}_5]\}=\{[-28\mathrm{.}2843],[-28\mathrm{.}2843],[27\mathrm{.}7380],[7\mathrm{.}1613],[0],[-50],[-15\mathrm{.}6661],[43\mathrm{.}0423]\}kN,\{[P_C],[P_D],[P_E],[P_F],[P_G]\}=\{[49\mathrm{.}8397],[17\mathrm{.}0424],[-47\mathrm{.}8764],[-27\mathrm{.}7380],[2\mathrm{.}5416]\}kN$