Let $A$ be the matrix:
$$\left(\begin{matrix} \alpha I_{n} \\ \beta I_{n} \end{matrix}\right)$$
where $\alpha,\beta\in\Bbb C$ are not both zero. Derive (a) the (reduced) QR factorization of $A$ and (b) the pseudoinverse of $A$.
Any help for the second question about pseudoinverse ?
Thanks in advance
NEW
I know that if 1) rank(A)=n then $A^{+} = (A^{T} A)^{-1} A^{T}$ and if 2) rank(A)=n=m then $A^{+} = A^{-1}$. I use the 1) and I found : $A^{+} = (a^{2} I_{n} + b^{2} I_{n})^{-1} $$\left(\begin{matrix} \alpha I_{n} \ \beta I_{n} \end{matrix}\right)$
note the second brackets is a matrix (1x2). How could I solve this ? Any help