9. Find the symmetric matrix A associated with the given quadratic form. A. x +223 +63122...
Find the symmetric matrix A associated with the given quadratic form 2x2-3y2+z2 - 4xz A=
Find the symmetric matrix A associated with the given quadratic form 2x2-3y2+z2 - 4xz A=
4. (a) Find the symmetric matrix A associated with the quadratic form, q = 5x - 4.1112+5x3, and compute the eigenvalues X, and 12 and the associated normalized eigenvectors e, and e2 of A. (b) Use the result of Part (a) to determine the spectral decomposition for A PAP. 22), and y. . wal. Rewrite q = (c) Let x = Py, where P is in Part (b), x = ( 5x - 4x32 +503 in y-variables, yı and y2.
Find the matrix A of the quadratic form associated with the equation. x² + y² – 9=0 A=
Exercise 2 Consider the symmetric matrix A a13 23 012 a13 023 , the quadratic form .q(z) = z'Az, associated T2 T3 1. Show that for x = with the symmetric matrix A is 2. Using the result from question (1), find the matrix associated with the quadratic forms below. Assumed that x is in IR3
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 point) Write the matrix of the quadratic form Q(x, y, z) = 2.02 + 3y2 – 2z2 + 2xy + x2 + 8yz. A=
1) Classify the following quadratic forms. (a) 9(x, y) = 2x2 + 3xy + 3y2 (b) q(x, y, z) = x2 + 3xy – xz + 3y2 – 2yz
Question 10 Find the matrix of the quadratic form associated with the quadratic equation 7x2 +1&xy – 2y2 -32=0. Selected Answer a
Find the matrix A of the quadratic form associated with the equation. 48x2 + 72xy + 27y2 - 74x - 52y + 70 = 0 A = Find the eigenvalues of A. (Enter your answers as a comma-separated list.) a = Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) P=
5.3.15 Consider the quadratic form tx In (5.3.21) 1) Find a symmetric matrix A E R(n, n) such that q(x)-x' Ax for (ii) Compute the eigenvalues of A to determine whether q or A is pos- r E R" itive definite,