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PC covariance

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Suppose that the random variables X1, X2 and X3 have the covariance matrix...
(i) Determine the three PC's based on ∑.
(ii) What percentage of the total variation is explained by each of the PC's
(iii) Calculate the correlation coefficients between the first PC and each of the variables X1, X2 and X3.
(iv) What are the PC's and their corresponding variances based in the respective covariance matrices for the sub-vectors
a) (X1, X2)T, and
b) (X1, X3)T?

Please see attached for full question.

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This solution shows how to work with a covariance matrix to determine PC's and correlation coefficients.

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