I have 2 vectors $u$ and $v$ given in $\mathbb R^4$, e.g. $u = (-1,-2,3,4)$ and $v=(1,-2,-3,5)$
I also have $Ax=b$ which is an under-determined system; meaning, if $A$ is $m\times n$, then $m\le n$.
We define a 2 dimensional plane as follows $K=\{x\in \mathbb R^4:\, u^Tx = 1,\,v^Tx = 1\}$.
I need to find the projection of some point $z = (1,2,2,1)$ on $K$ plane by formulating a least-norm problem.
I know that I can use $x=A'(AA')^{-1}\setminus b$ this formula to solve the least-norm problem.
Thanks