= Solution
Using divisor $n=4$, the <covariance matrix> is
$$
\boxed{\Sigma=\frac14X_c^{\mathsf T}X_c=
\begin{pmatrix}3&1&2\\1&3&2\\2&2&4\end{pmatrix}}.
$$
For example, the first <variance> is $(1+1+1+9)/4=3$, and the first-second <covariance> is $(3-1-1+3)/4=1$. If “sample <covariance matrix>” means the unbiased convention, use divisor $n-1=3$ instead: $S=(4/3)\Sigma$. This multiplies every <eigenvalue> by $4/3$ and leaves all <principal component loadings> and explained-<variance> fractions unchanged.
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