Generalized solutions for the smallest Euclidean norm

[crazygrey]

Hi folks,

I have to find the generalized solution for the following Ax=y :

[1 2 3 4;0 -1 -2 2;0 0 0 1]x=[3;2;1]

The rank of A is 3 so there is one nullity so the generalized solution is:

X= x+alpha.n (where alpha is a constant , and n represents the nullity)

I found the solution to be:

X= [-1;0;0;1]+ alpha [1;-2;1;0] which is a non-unique solution.

I need to find (alpha) so that the generalized solution, i.e, the eigenvector has the smallest Euclidean norm

Thanks

 

[crazygrey]

Any help ?