The problem is to minimize $$f(x) = x^T.x$$
subject to condition $$Ax = b$$
With the help of Lagrange Multipliers, which gives the equation $$L(x,\lambda) = x^Tx + {\lambda}^T(Ax-b)$$
The solution here would be $${\delta}_x L(x,\lambda) = 0$$
Which gives the $x$ value that minimizes $f(x)$. Thus $$ 2x+A^T\lambda = 0$$ $$=> x = -\frac 12A^T\lambda$$
What am not able to figure out is the following:
the significance of the $\lambda$ value obtained by differentiating the langrange, which means $${\delta}_{\lambda} L(x,\lambda) = 0$$ $$ => Ax - b = 0$$ and subsituting x , we get $$\lambda = -2({A{A^T}})^{-1}b$$
What is the dual problem here?
Please kindly help me.