2
= 2
{scope}
Throughout Question 2(a) and 2(b), write $U=[u_1,\ldots,u_n]$, $V=[v_1,\ldots,v_n]$, and $\Sigma=\operatorname{diag}(\sigma_1,\ldots,\sigma_n)$. Then the supplied full <singular value decomposition> can also be written $A=U\Sigma V^T$, with $U^TU=V^TV=I_n$ and $[U,U_\perp]$ an $m\times m$ <orthogonal matrix>.