Solution
= Solution
Here
$$
A^\dagger A=\frac12\begin{pmatrix}5&-3\\-3&5\end{pmatrix},
$$
with <eigenvalues> $4,1$ and corresponding normalized <vectors> $(1,-1)^T/\sqrt2$ and $(1,1)^T/\sqrt2$. A compatible choice is
$$
U=\frac1{\sqrt2}\begin{pmatrix}1&1\\-1&1\end{pmatrix},
\qquad
V=\begin{pmatrix}1&0\\0&-1\end{pmatrix},
\qquad
D=\begin{pmatrix}2&0\\0&1\end{pmatrix}.
$$
Direct multiplication gives $V^\dagger AU=D$.