I have $\begin{align} A &= \begin{bmatrix} 2 \\ 3 \\ \vdots \\ \sqrt{5n-1} \end{bmatrix} \end{align} $*$\begin{align} \begin{bmatrix} -1& 1 & ... & (-1)^n \end{bmatrix}^* \end{align}$
And I want to compute Moore–Penrose inverse matrix of A. That is $A^+$.
My attempts: definition with limits $A^+ = \lim_{\delta \to +0} (A^* A + \delta I)^{-1} A^*$. This doesn't work because I have no idea in computing inverse matrix with parameter and $A^*A$ is not invertible. Also I can say that $A$ is not invertible, so I can't consider that $A^+=A^{-1}$.
Can you help me with this problem?