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Given the measurements of two quality characteristics as below. 1) Find the correlation coefficient r between x1 and x2. 2) The correlation between x1 and x2 can be expressed using a matrix form, R=[1rr1], Find the eigenvalues and eigenvectors of R. 3) Using the eigenvectors to form the transformation matrix Q, then the variables x1 and x2 can be transformed into independent variable u1, and u2, by [u1u2]=Q[Sx1x1x1Sx2x2x2] where Sxi,i=1,2 are sample standard deviations of xi,i=1,2 (i.e. sample estiamtors of the respective standard deviations). Calculate the corresponding values of u1, and u2 for all time steps