with xtau = {-2 -5}T

I found the gradient of f(xtau) to be {4x1 -2x2}T, which using xtau turns into {-8 10}.

I computed the gradients of g1(x) and g2(x) to be:

gradient g1(x) = {2x1 -1}T

gradient g2(x) = {-1 1}T

Correct so far?

From this, I get a bit confused when setting up the computation for the Lagrange multiplier (meaning I don't get an answer that matches one of the possible choices).

My understanding is that it should be:

gradient of f(x) + lambda1*gradient of g1(x) + lambda2*gradient of g2(x) = 0 matrix

In Matlab I enter the following:

b = [-8; 10];

A = [-4, 0; -1, 0];

x = A \ b; % to compute least squares

At this point, I get {-0.4 9.6}T which doesn't appear to be correct.

Any help in understanding what I'm doing wrong will be appreciated.

Thanks!