VontLet Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ - 12x₁ x3 +24x2x3. Find a unit vector x in R3 at which Q(x) is maximized, subject toTx'x= 1.[Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]A unit vector that maximizes Q(x) is u =(Type an exact answer, using radicals as needed.)

Answered: Image /qna-images/answer/bf88dc35-358a-4641-9c14-45bb2c87e240.jpg

Answered: Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Use the Jacobi iterative method (Vector-Matrix Form) with r0) = (2, 2) to solve the linear system. Find one iteration only. 5x1 – 3r2 = 7 -4x1 + 7x2 = -1
Describe all least-squares solutions of the equation Ax = b. 重 110 1 110 b 10 1 A = 101 12 The general least-squares solutions of Ax = b for the given matrix A and vector b are all vectors of the form x =+x (Simplify your answers.) with x, free.
(3) Let matrix A have eigenvectors . . associated with eigenvalues Xo = 4, A₁ = 2, A₂ = 0), respectively. Suppose some vector 7 is: 7 = №n +27₁ +30¹₂ Compute Ar. Give your result as a linear combination of eigenvectors ₁.
Express the quadratic form T as v Av, where A is a symmetric matrix. x² + 3y² + 5z² − 4xy+3yz + 10xz
Consider the following interpolating points for the function f(x) = x² – 2x: Xi 01 23 f(xi) 0 -1 03 (a) Use monomial basis to find P₁(x) that interpolates f(x) at x; for i = 0,1. Con- struct the Vandermonde matrix and then use the backslash \ in matlab to solve the linear system. (b) Repeat (a) to find P₂(x) that interpolates f(x) at x; for i = 0, 1, 2. (c) Repeat (a) to find P3(x) that interpolates f(x) at x, for i = 0, 1, 2, 3. (d) Compare P₂(x), P3(x) and f(x). What do you see? Can you explain it?
Compute the quadratic form x' Ax for A = X1 5 444 X2 -9 x3 a. x = a. x¹ Ax= b. x' Ax= C. X' Ax= 1/√√3 b. x= 7 C. X = - 1/√3 1/√√3 (Simplify your answer.) 360 643 035 (Simplify your answer.) and each of the following vectors.
b) Consider the matrix TM UTM UTM UTM -1 21 A = OTM UTM 7TMUTM UTM 4 i. Compute the dominant eigenvalue, di and the corresponding eigen- -4 20 UT vector x1 for the matrix A using power method starting with x0) = (1, 1, 1)" and stop the iterations when |mg+1 – mel < 0.05. AUTM %3D ii. Determine the smallest eigenvalue, Az for matrix A by using shifted power method based on the results in (i). Start the iteration with initial vector x) = (1,0,0)" and stop the iterations when ||x*+1) – x*)|| < 0.05. TM UTM UTM (k) %3D
Derive the normal equations for the least-squares cubic f(x) =Ax 3+ Bx 2+ Cx + D.
Find a formula for the least-squares solution of Ax =b when the columns of A are orthonormal.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ −12x₁ x3 +24X2X3. Find a unit vector x in R³ at which Q(x) is maximized, subject to xJx=1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]