Question 10: Consider a dataset {x_1, x_2, x_3, x_4}, where each x_i …

Consider a dataset $\{x_1, x_2, x_3, x_4\}$, where each $x_i \in \mathbb{R}^3$. The covariance matrix $C$ has three non-zero eigenvalues $\lambda_1 > \lambda_2 > \lambda_3$ satisfying:

$2\lambda_1 - \lambda_2 + \lambda_3 = 8$

$\lambda_1 + 2\lambda_2 - \lambda_3 = 5$

The difference between the largest and smallest eigenvalue is 3. Determine the total variance of the dataset.