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4. Diagonalize the quadratic form: Q = 8x} + 12x, X2 - 8xz a) Give its matrix A. b) Give the diagonal matrix D, and the new diagonalized quadratic form ( as a function of the new coordinate vector y = [v1.y2] 6 det la - D 6 -:- 1) = 12 – 100 = 0 => 1 = +10 = D = 110_) QC) = 10y - 10y3 c) Give an orthogonal diagonalizing transformation matrix P(cols P are the basis in which Q becomes 0). (A – 1076 = 1.3 -18] : = 7 = = [] works & v = ( 3' is orthog to it =P = 3') works. 0 P d) Give an equation showing the relationship between the old x = [X1, X2]and the new ý = [y..y2] coordinates. * PDP=y"Dy pe=Ÿ or x = Py