Problem $3(30$ points$)$: Given that the space frame $\backslash ($ A B C D E $\backslash )$ is supported by a ball and socket at $\backslash ($ B $\backslash )$ and short links at $\backslash ($ C$,$ D $\backslash ),$ and $\backslash ($ E $\backslash ),$ use your FBD from HW $1$ or from HW$1$ solutions to:

a$)$ develop a set of equilibrium equations for the space frame,

b$)$ create the coefficient matrix, $\backslash (\backslash$mathbf$\{$A$\}\backslash ),$ and the constants vector $\backslash (\backslash$mathbf$\{$b$\}\backslash ),$ and

c$)$ use $\backslash (\backslash$mathbf$\{$x$\}=\backslash$mathbf$\{$A$\}^\{-1\}\backslash$mathbf$\{$b$\}\backslash )$ to find the unknown forces at $\backslash ($ B $\backslash ),\backslash ($ C$,$ D $\backslash ),$ and $\backslash ($ E $\backslash )$