Let Q(x)- 355x35x3 -40x,*2 20x,X3+40x2X3 Find a unit vector x in R3 at which Q(x) 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)...
linear algebra question 1. Let Q(x) = 3x1 X2 + 5X1 x3 + 7X1 X4 + 7x2 x3 + 5x2 x4 + 3x3 n Find the maximum value Q(x) subject to the constraint xx 1, and find a unit vector u this maximum is obtained. a. 1 and xu o. b. Find the maximum value Q(x) subject to the constraintx
a 0 0 where a b, and c are positive numbers. Let S be the unit ball whose bounding surface has the equation x-x R3 + R3 be a linear transformation determined by the matrix A= 1 Complete Let 0 b 0 + x 0 0 c parts a and b below. u1 x1 2 ,2 2 a Show that T S is bounded by the ellipsoid with the equation 1 Create a vector u = that is within set...
7 4 Find a unit vector in the direction of 3 2 1 A unit vector in the direction of the given vector is (Type an exact answer, using radicals as needed.).
Find the directions in the xy-plane in which the function fixy) 15-2x2 -y2 has zero change at the point P(2,1,3) Express the directions in terms of unit vectors What is the unt vector in a direction of zero change with a positive x-component? Type exact answers, using radicals as needed.) What is the other unit vector in a direction of zero change? (Type exact anowers, using radicals as needed.) cess Ubrary Enter your answer in each of the answer boxes...
#8 6.3.15 6 -3 -2 Let y = u- U2 - 1 Find the distance from y to the plane in R3 spanned by u, and uz: 3 1 -2 The distance is (Type an exact answer, using radicals as needed.)
Find the best approximation to z by vectors of the form C7 V + c2V2. 3 1 3 -1 -6 1 z = V2 4 0 -3 3 1 The best approximation to z is . (Simplify your answer.) - 15 - 8 8 - 1 Let y = , and v2 Find the distance from y to the subspace W of R* spanned by V, and vą, given 1 0 1 - 15 3 3 - 13 09 that...
Find the complex zeros of the following polynomial function. Write fin factored form. f(x) = x3 - 13x² + 59x - 87 The complex zeros off are (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations) Question (7) Consider...
3. Let M2.2 be the vector space of 2 x 2 matrices. Let a) Find a spanning set of U. b) What is the size of the smallest spanning set of U? c) Find a matrix A ? M2.2 such that A .