import numpy as np

theta=np.pi/4.0   					# angle marked theta in Figure Q.2(a)

F = np.array([[-1.0,0,0,0,0,0,0,0], # sum of horizontal forces node 1
           [0,0,0,0,-1.0,0,0,0], 	# sum of vertical forces node 1
 		  [1.0,0,np.cos(theta),0,0,0,0,0],		# sum of horizontal forces node 2
 		  [0,-1.0,-np.sin(theta),0,0,0,0,0],	# sum of vertical forces node 2
 		  [0,0,0,1.0,0,0,0,0],
 		  [0,1.0,0,0,0,1.0,0,0],
 		  [0,0,-np.cos(theta),-1.0,0,0,0,1.0],
 		  [0,0,np.sin(theta),0,1.0,0,1.0,0]])
E = np.array([-1000.0,0,0,0,0,0,0,0]) # sum of external loads
x = np.linalg.inv(F).dot(E)
print(x)