node $1$:

${\displaystyle \underset{?}{\overset{?}{}}}{F}_H-0,,-F_{1}cos30+F_{3}cos60+F_{1,h}=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_V=0,,-F_{1}sin30-F_{3}sin60+F_{1,v}=0$

for node $2$ :

${\displaystyle \underset{?}{\overset{?}{}}}{F}_H=0,F_2+H_2+F_{1}cos30+F_{2,h}=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_V=0,V_2+F_{1}sin30+F_{2,v}=0$

for node $3$ :

${\displaystyle \underset{?}{\overset{?}{}}}{F}_H=0-F_2-F_{3}cos60+F_{3,h}=0$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_V=0V_3+F_{3}sin60+F_{3,v}=0$

$1.($points $10)$ use python to Express this set of linear algebraic equations in matrix form

$2.($points $15)$ Then, use Python to solve for the forces and reactions for the case displayed

in Fig. $1$

i$.$ using the inverse of the coefficients matrix: numpy.linalg.inv

ii$.$ using directly the command: numpy.linalg.solve

iii. using LU factorization: scipy.linalg.lu

iv$.$ how do the solutions of the items above compare to each other?

$3.($points $5)$ Determine the system$$s matrix inverse.