Question $3$: Truss problem

According to the truss problem described below, formulate the linear system $Ax=b.$ Consider the following plane truss having $3$ members connected by $3$ joints. We would like to determine the resulting force on each member of the truss.

Use $d=15.$

Using the following static equilibrium equations, cast the system of linear equations into a matrix equation $A^{**}x=b,$ such that A is the matrix of coefficients, b is the load vector $($right hand side vector$),$ and x is the vector of unknown forces.

For joint $1$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0=>1000sin(d)+F_{1}cos(30)+F_{3}cos(60)=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0=>-1000cos(d)+F_{1}sin(30)+F_{3}sin(60)=0$

For joint $2$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0=>H_2-F_{1}cos(30)-F_2=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0=>V_2-F_{1}sin(30)=0$

For joint $3$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0=>F_2+F_{3}cos(60)=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0=>V_3-F_{3}sin(60)=0$

Solve for the unknowns: F$1,$ F$2,$ F$3,$ H$2,$ V$2,$ V$3(6$ unknows.$)$

Display your results.