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(1 point) Write the matrix of the quadratic form Q(x, y, z) = 2.02 + 3y2...
1) Classify the following quadratic forms. (a) 9(x, y) = 2x2 + 3xy + 3y2 (b) q(x, y, z) = x2 + 3xy – xz + 3y2 – 2yz
10') Determine the range of a so that the quadratic form Q(x, y, z) = a(r+y+z)+2xy-2yz+2zx positive definite.
Consider the quadratic form Q - 2u24u,u2 5u22 + 2uzu32u,u 8. Write the quadratic form with the help of a matrix, in the form XAX 9. Examine whether the "definitness" of this quadratic form 10. BONUS (1 point). Calculate the eigenvalues of the discriminant and use them to check your answer to question 9
Consider the quadratic form Q - 2u24u,u2 5u22 + 2uzu32u,u 8. Write the quadratic form with the help of a matrix, in the form XAX 9....
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=
9. Find the symmetric matrix A associated with the given quadratic form. A. x +223 +63122 B. 2x2 – 3y2 + x2 - 4x2
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e e-3x2 – 3y2 – 2z2 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e e-3x2 – 3y2 – 2z2 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
Find an orthogonal change of variables that eliminates the cross product terms in the quadratic form Q, and express Q in terms of the new variables. 7x{ + 6x2 + 5x3 - 4X1X2 + 4x2X3 A substitution x = Py that eliminates cross-product terms is X1 = o A substitution x = Py that eliminates cross-product terms is Xi = – -}y.+3y2– žys, x2 = - - Žy2+3y2 +3v3, x3 = - {yı+ {y2– žv3. The new quadratic form is...
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)...