Question 10: Let \mathbf{C} be the covariance matrix of a mean-center…

Let $\mathbf{C}$ be the covariance matrix of a mean-centered dataset:

$\mathbf{C} = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$

Standard PCA is performed on this dataset. The first two PCs are given below:

$\mathbf{w}_1 = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ 1 \end{bmatrix} \quad \mathbf{w}_2 = \frac{1}{\sqrt{2}} \begin{bmatrix} -1 \\ 1 \end{bmatrix}$

Based on the above data, answer the given subquestions.