for this question, i do not know how to find a linear transformation L

Let X = [X1, X2] denote a Gaussian random vector with mean ux = [0, a] and covari- ance Ex = 4 2 2 2 for some a E R . Verify that Ex is a valid covariance matrix. . What is the marginal pdf fx, (x1) for X1? . Find the conditional density function fx,X2(X1/x2) . Find a linear transformation L defining two new variables Y1, Y2 such that they are uncorrelated to one another subject to the constraint that LL" = I: [Y1, Y2] = L [X1, X2] . Are Y1 and Y2 also statistically independent