### (a) Analytically calculate the covariance matrix of ~x

x1^2 x1*x2 x1(x1 + x2)
x2*x1 x2^2 x2(x1 + x2)
x1(x1 + x2) (x1 + x2)x2 (x1 + x2)^2

### (b) What are the eigenvalues?

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(c) Numerically verify these results by drawing a data set from the distribution and computing the covariance matrix and eigenvalues.

### (d) Numerically find the eigenvectors of the covariance matrix, and use them to construct a transformation to a new set of variables ~y that have a diagonal covariance matrix with no zero eigenvalues. Verify this on the data set.