For the truss shown below, the support at $A$ is a roller, and $C$ is a pin. $E=30{10}^6\frac{lb}{i}{n}^2.$

$A_1=A_2=0\mathrm{.}6i{n}^2,A_3=0\mathrm{.}9i{n}^2.$ The numbers in red and blue are used to label the degree of freedom $($DOF$)$ and the members, respectively.

Using the numbering of DOFs and members and direction of each member shown in the figure, use the stiffness method to compute:

a$.$ Element stiffness matrix for each member in the global coordinate: $k_1,k_2,k_3.$

b$.$ The structure stiffness matrix $K_{FF}$ for all the free DOFs.

c$.$ Displacements at all the free DOFs: ${}_1,{}_2,$ and ${}_3.$

d$.$ Member forces: $F_1,F_2,$ and $F_3.$

e$.$ Support Reactions: $A_x,C_x,$ and $C_y.$