Advanced mathematics, problems about Lagrange multiplier method. Does this method list λ≠0 in the process of solving equations? If there is no such condition, why?
λ≠0 is the prerequisite for Lagrange multiplier method to find the extreme value of multivariate function. In fact, λ=0 corresponds to the unconditional extremum problem (in your example, λ=0 becomes the unconditional extremum of the function f (x, y) = 1/2 * (x+y-8) 2).