= Solution
{c}
Take the <identity matrix>
$$
A=\begin{pmatrix}1&0\\0&1\end{pmatrix},\qquad
B_1=\begin{pmatrix}1&0\\0&0\end{pmatrix},\qquad
B_2=\begin{pmatrix}0&0\\0&1\end{pmatrix}.
$$
Both $B_1$ and $B_2$ have <matrix rank> one, and
$$
\|A-B_1\|_2=\|A-B_2\|_2=1=\sigma_2(A).
$$
They are distinct and both attain the minimum <spectral norm> error from the preceding part. Hence \b[a best <low-rank approximation> of rank one need not be unique]. More generally, every <orthogonal projection> $uu^T$ with $\|u\|_2=1$ gives another such minimizer.
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