srg = srange(-4,4,1/10,include_endpoint=True)
@interact
def dualv(a1=slider(srg,default=1),a2=slider(srg,default=2), a3=slider(srg,default=-1),a4=slider(srg,default=3)):
A1 = arrow2d([0,0],[a1,a2],rgbcolor='black')
A2 = arrow2d([0,0],[a3,a4],rgbcolor='black')
A3 = arrow2d([0,0],[a1,a3],rgbcolor='black')
A4 = arrow2d([0,0],[a2,a4],rgbcolor='black')
p1 = polygon([[0,0],[a1,a2],[a1+a3,a2+a4],[a3,a4],[0,0]], alpha=.5)
p2 = polygon([[0,0],[a1,a3],[a1+a2,a3+a4],[a2,a4],[0,0]],rgbcolor='red', alpha=.5)
A = matrix([[a1,a2],[a3,a4]])
html('<h3>The determinant of a matrix is equal to the determinant of the transpose</h3>')
html("$det(%s) = det(%s)$"%(latex(A),latex(A.transpose())))
show(A1+A2+A3+A4+p1+p2)
