Linear algebra

Application/Analysis (Technology allowed, show all relevant work!) Let A be the symmetric matrix } : a) Find the eigenvalues and the eigenvectors b) Construct the matrix P, and then modify the matrix P so that it becomes an orthogonal matrix with determinant equal to 1. Also compute the counterclockwise angle of rotation (5 points). c) Now suppose that you are given the following quadratic form associated with the original matrix A: 5x2 + 4xy + 8y? = 36 Write down the resulting quadratic form in terms of U and V [Note: There is hardly any work to show on this one!] d) Sketch the graph of the resulting curve, also showing the U and V axes in relationship to the x and y axis