Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form...
Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. -5x2 - 12x4x2 What is the most precise classification for the quadratic form? O A. Positive definite O B. Indefinite O C. Negative semidefinite OD. Positive semidefinite O E. Negative definite The new quadratic form is y'Dy=N.
(2) Express the quadratic form Q=x; -x} - 4x,x2 + 4xzxz in terms of diagonal quadtratic form.Use X(X1, X2, X3)=PY(y1,92,93) 121 Tannster.T.D-D alhym2) - (2. Ihim
Consider the quadratic form Q(x) xỈ + x2 + x + 4X1X2 + 4x2x3 + 4x3x1. (a) Find the real symmetric matrix A so that Q(X) = XTAX. (b) Find an orthogonal matrix Q so that the change of variables x = Qy transforms the quadratic for Q(x) into one with no cross-product terms, that is, diagonalize the quadratic form (x). Give the transformed quadratic form. (c) Find a vector x of length 1 at which Q(x) is maximized. (d)...
# 1: Consider the following curves in R la) 1822-32 x y + 37 U2 100. l ) 2x2 + 6 x y + 2 y-100. 1c) x2 + 4 x y + 4 y2-10:0. Write them in normal form. Give the change of variables that does this. For example, in 1a) the orthonormal basis of eigenvectors are λί 5,V1 (2,1)'/V5 and λ2 = St ( 100. ) . That is, 45, ½ = (1,-2)t/V5.S ( 1/V 5-2/v/5 ) (V6,...