1) Classify the following quadratic forms. (a) 9(x, y) = 2x2 + 3xy + 3y2 (b)...
(1 point) Write the matrix of the quadratic form Q(x, y, z) = 2.02 + 3y2 – 2z2 + 2xy + x2 + 8yz. A=
9. Find the symmetric matrix A associated with the given quadratic form. A. x +223 +63122 B. 2x2 – 3y2 + x2 - 4x2
(45). (Symmetric Matrices and Quadratic Forms) Examine the following functions for relative extremum values: (a) F = x²y + 2.2 – 2xy + 3y2 – 4.c + 7y (b) F = 73 + 4.x2 + 3y² + 52 - 6y
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
Problem #10: Consider the following function. 8(x,y) = {2x2 – 3y2 +6V6 y (a) Find the critical point of g. If the critical point is (a, b) then enter 'ab' (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (c) Use the Second Partials test to classify the critical point from (a). Problem #10(a): Enter your answer...
Find the partial derivative. Find fx (-2,3) when f(x,y) = 2x2 – 3xy - y. O A. - 10 B. 15 C. -9 OD. 14
10') Determine the range of a so that the quadratic form Q(x, y, z) = a(r+y+z)+2xy-2yz+2zx positive definite.
8. Determine whether the following functions reach a maximum or minimum and the values of x and y for a maximum or minimum. a) Z(x, y) = x2 + 3y2 - 3xy b) W(x, y, z) = 29-(x2 + y2 + 22)
Quadratic forms arise often in geometry, physics and engineering and it is desirable to reduce these to canonical (standard) forms. Reduce the quadratic form:Q = 3x12 + 5 x22 + 3x32 - 2x2 x3 + 2x1 x3 - 2 x1 x2 to a standard form by making an approximate change in variables X = MY , where M is an orthogonal matrix. i) Write Q as X T AX . ii) Find the Eigenvalues of A. Is the quadratic form...
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...