= A centered dataset with n = 90 observations and p · 6 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ was generated 1 0.339 -0.01 -0.154 0.025 -0.024 0.339 1 -0.153 -0.12 -0.03 -0.098 -0.01 -0.153 1 0.123 0.088 0.137 -0.154 -0.12 0.123 1 0.243 0.081 0.025 -0.03 0.088 0.243 1 0.025 -0.024 -0.098 0.137 0.081 0.025 A) Compute and write the numerical value of the eigenvalue 13 of Σ. This eigenvalue is located in the position (3, 3) of the matrix A and is simultaneously the sample variance of the score PC3: B) Compute and write the percentage of total variability explained by the Principal component PC3. The number you write should be between 0 and 100 and you should include decimals in your answer. C) As seen in lectures, the eigenvalue 13 is related to d3, one singular value of the data matrix X. Compute and write the value of d3.

= A centered dataset with n = 90 observations and p · 6 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ was generated 1 0.339 -0.01 -0.154 0.025 -0.024 0.339 1 -0.153 -0.12 -0.03 -0.098 -0.01 -0.153 1 0.123 0.088 0.137 -0.154 -0.12 0.123 1 0.243 0.081 0.025 -0.03 0.088 0.243 1 0.025 -0.024 -0.098 0.137 0.081 0.025 A) Compute and write the numerical value of the eigenvalue 13 of Σ. This eigenvalue is located in the position (3, 3) of the matrix A and is simultaneously the sample variance of the score PC3: B) Compute and write the percentage of total variability explained by the Principal component PC3. The number you write should be between 0 and 100 and you should include decimals in your answer. C) As seen in lectures, the eigenvalue 13 is related to d3, one singular value of the data matrix X. Compute and write the value of d3.