# Linear combination of vectors

v = np.array([[3],[1]])
w = np.array([[-2],[-4]])

a = 1.5
b = 1

vec_new = a*v + b*w

print(vec_new)

[[ 2.5]
 [-2.5]]

origin = np.zeros(vec.shape)

plt.figure(figsize=(6,6))
plt.quiver(*origin, *vec_new, color=['r'], scale=1, units='xy')
plt.quiver(*origin, *v, color=['g'], scale=1, units='xy')
plt.quiver(*origin, *w, color=['b'], scale=1, units='xy')

plt.grid()
plt.xlim(-5,5)
plt.ylim(-5,5)
plt.text(v[0], v[1], 'v')
plt.text(w[0], w[1], 'w')
plt.text(vec_new[0], vec_new[1], 'Linear combination of a*v and b*w')
plt.gca().set_aspect('equal')
plt.show()