Problem $3(16$ points$)$: Use your free body diagram from HW $1$ to:

a$)$ develop a set of equations for the beam $\backslash ($ A B C D E $\backslash )$ that could be used to find the unknown forces at $\backslash ($ A $\backslash )$ and $\backslash ($ D $\backslash ),$

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

c$)$ find the unknown forces at $\backslash ($ A $\backslash )$ and $\backslash ($ D $\backslash ).$